KILLED proof of input_oCNgudFnGd.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 51 ms] (6) CdtProblem (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxRelTRS (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (12) typed CpxTrs (13) OrderProof [LOWER BOUND(ID), 7 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 44.0 s] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 14 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 57 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 689 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 69 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 287 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 46 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 347 ms] (30) typed CpxTrs (31) RewriteLemmaProof [LOWER BOUND(ID), 161 ms] (32) typed CpxTrs (33) RewriteLemmaProof [LOWER BOUND(ID), 15.5 s] (34) BEST (35) proven lower bound (36) LowerBoundPropagationProof [FINISHED, 0 ms] (37) BOUNDS(n^1, INF) (38) typed CpxTrs (39) RewriteLemmaProof [LOWER BOUND(ID), 5554 ms] (40) typed CpxTrs (41) RewriteLemmaProof [LOWER BOUND(ID), 27.2 s] (42) typed CpxTrs (43) RewriteLemmaProof [LOWER BOUND(ID), 16.1 s] (44) typed CpxTrs (45) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (46) CdtProblem (47) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CpxRelTRS (51) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (52) CpxTRS (53) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CpxWeightedTrs (55) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CpxTypedWeightedTrs (57) CompletionProof [UPPER BOUND(ID), 0 ms] (58) CpxTypedWeightedCompleteTrs (59) NarrowingProof [BOTH BOUNDS(ID, ID), 1841 ms] (60) CpxTypedWeightedCompleteTrs (61) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (62) CpxRNTS (63) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CpxRNTS (65) CompletionProof [UPPER BOUND(ID), 0 ms] (66) CpxTypedWeightedCompleteTrs (67) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (68) CpxRNTS (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (76) CdtProblem (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 24 ms] (80) CdtProblem (81) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (96) CdtProblem (97) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms] (100) CdtProblem (101) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 36 ms] (116) CdtProblem (117) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 6 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms] (126) CdtProblem (127) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 55 ms] (132) CdtProblem (133) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 9 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 35 ms] (138) CdtProblem (139) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 31 ms] (144) CdtProblem (145) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 5 ms] (152) CdtProblem (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 42 ms] (158) CdtProblem (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 2 ms] (160) CdtProblem (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 31 ms] (162) CdtProblem (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (166) CdtProblem (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (170) CdtProblem (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (172) CdtProblem (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 135 ms] (174) CdtProblem (175) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 55 ms] (178) CdtProblem (179) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (180) CdtProblem (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 98 ms] (182) CdtProblem (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 9 ms] (184) CdtProblem (185) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 169 ms] (186) CdtProblem (187) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (188) CdtProblem (189) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 92 ms] (190) CdtProblem (191) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 27 ms] (192) CdtProblem (193) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 204 ms] (194) CdtProblem (195) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 36 ms] (196) CdtProblem (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 102 ms] (198) CdtProblem (199) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 24 ms] (200) CdtProblem (201) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 106 ms] (202) CdtProblem (203) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (204) CdtProblem (205) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 150 ms] (206) CdtProblem (207) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 39 ms] (208) CdtProblem (209) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 159 ms] (210) CdtProblem (211) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (212) CdtProblem (213) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 164 ms] (214) CdtProblem (215) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 52 ms] (216) CdtProblem (217) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 148 ms] (218) CdtProblem (219) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 36 ms] (220) CdtProblem (221) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 305 ms] (222) CdtProblem (223) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 16 ms] (224) CdtProblem (225) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 261 ms] (226) CdtProblem (227) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 39 ms] (228) CdtProblem (229) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 370 ms] (230) CdtProblem (231) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 39 ms] (232) CdtProblem (233) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 198 ms] (234) CdtProblem (235) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 65 ms] (236) CdtProblem (237) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 292 ms] (238) CdtProblem (239) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 55 ms] (240) CdtProblem (241) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 220 ms] (242) CdtProblem (243) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 59 ms] (244) CdtProblem (245) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (246) CpxWeightedTrs (247) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (248) CpxTypedWeightedTrs (249) CompletionProof [UPPER BOUND(ID), 0 ms] (250) CpxTypedWeightedCompleteTrs (251) NarrowingProof [BOTH BOUNDS(ID, ID), 151 ms] (252) CpxTypedWeightedCompleteTrs (253) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (254) CpxRNTS (255) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (256) CpxRNTS (257) CompletionProof [UPPER BOUND(ID), 0 ms] (258) CpxTypedWeightedCompleteTrs (259) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (260) CpxRNTS ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N))) a__sqr(0) -> 0 a__sqr(s(X)) -> s(a__add(a__sqr(mark(X)), a__dbl(mark(X)))) a__dbl(0) -> 0 a__dbl(s(X)) -> s(s(a__dbl(mark(X)))) a__add(0, X) -> mark(X) a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) a__first(0, X) -> nil a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(X))) -> s(a__half(mark(X))) a__half(dbl(X)) -> mark(X) 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(half(X)) -> a__half(mark(X)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(recip(X)) -> recip(mark(X)) mark(s(X)) -> s(mark(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) a__half(X) -> half(X) 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(a__add(a__sqr(mark(X)), a__dbl(mark(X)))) a__dbl(0') -> 0' a__dbl(s(X)) -> s(s(a__dbl(mark(X)))) a__add(0', X) -> mark(X) a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) a__first(0', X) -> nil a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) a__half(0') -> 0' a__half(s(0')) -> 0' a__half(s(s(X))) -> s(a__half(mark(X))) a__half(dbl(X)) -> mark(X) 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(half(X)) -> a__half(mark(X)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(recip(X)) -> recip(mark(X)) mark(s(X)) -> s(mark(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) a__half(X) -> half(X) 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(a__add(a__sqr(mark(X)), a__dbl(mark(X)))) a__dbl(0) -> 0 a__dbl(s(X)) -> s(s(a__dbl(mark(X)))) a__add(0, X) -> mark(X) a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) a__first(0, X) -> nil a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(X))) -> s(a__half(mark(X))) a__half(dbl(X)) -> mark(X) 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(half(X)) -> a__half(mark(X)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(recip(X)) -> recip(mark(X)) mark(s(X)) -> s(mark(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) a__half(X) -> half(X) 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(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__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__SQR(z0) -> c5 A__DBL(0) -> c6 A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__DBL(z0) -> c8 A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c12 A__FIRST(0, z0) -> c13 A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__FIRST(z0, z1) -> c15 A__HALF(0) -> c16 A__HALF(s(0)) -> c17 A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) A__HALF(z0) -> c20 MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) MARK(0) -> c32 MARK(nil) -> c33 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__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__SQR(z0) -> c5 A__DBL(0) -> c6 A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__DBL(z0) -> c8 A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c12 A__FIRST(0, z0) -> c13 A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__FIRST(z0, z1) -> c15 A__HALF(0) -> c16 A__HALF(s(0)) -> c17 A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) A__HALF(z0) -> c20 MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) MARK(0) -> c32 MARK(nil) -> c33 K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__TERMS_1, A__SQR_1, A__DBL_1, A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1 Compound Symbols: c_2, c1, c2, c3_3, c4_3, c5, c6, c7_2, c8, c9_1, c10_2, c11_2, c12, c13, c14_1, c15, c16, c17, c18_2, c19_1, c20, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c32, c33 ---------------------------------------- (7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__TERMS(z0) -> c1 A__SQR(0) -> c2 A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__SQR(z0) -> c5 A__DBL(0) -> c6 A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__DBL(z0) -> c8 A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c12 A__FIRST(0, z0) -> c13 A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__FIRST(z0, z1) -> c15 A__HALF(0) -> c16 A__HALF(s(0)) -> c17 A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) A__HALF(z0) -> c20 MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) MARK(0) -> c32 MARK(nil) -> c33 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(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(n^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__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__SQR(z0) -> c5 A__DBL(0') -> c6 A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__DBL(z0) -> c8 A__ADD(0', z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c12 A__FIRST(0', z0) -> c13 A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__FIRST(z0, z1) -> c15 A__HALF(0') -> c16 A__HALF(s(0')) -> c17 A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) A__HALF(z0) -> c20 MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) MARK(0') -> c32 MARK(nil) -> c33 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0') -> 0' a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0', z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0') -> 0' a__half(s(0')) -> 0' a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(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__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__SQR(z0) -> c5 A__DBL(0') -> c6 A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__DBL(z0) -> c8 A__ADD(0', z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c12 A__FIRST(0', z0) -> c13 A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__FIRST(z0, z1) -> c15 A__HALF(0') -> c16 A__HALF(s(0')) -> c17 A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) A__HALF(z0) -> c20 MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) MARK(0') -> c32 MARK(nil) -> c33 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0') -> 0' a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0', z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0') -> 0' a__half(s(0')) -> 0' a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' mark(nil) -> nil Types: A__TERMS :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c:c1 c :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c:c1 A__SQR :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c2:c3:c4:c5 mark :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil MARK :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c1 :: c:c1 0' :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c2 :: c2:c3:c4:c5 s :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c3 :: c9:c10:c11:c12 -> c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__ADD :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c9:c10:c11:c12 a__sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c4 :: c9:c10:c11:c12 -> c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__DBL :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c6:c7:c8 c5 :: c2:c3:c4:c5 c6 :: c6:c7:c8 c7 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c6:c7:c8 c8 :: c6:c7:c8 c9 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c10 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c11 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c12 :: c9:c10:c11:c12 A__FIRST :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c13:c14:c15 c13 :: c13:c14:c15 cons :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c14 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c13:c14:c15 c15 :: c13:c14:c15 A__HALF :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c16:c17:c18:c19:c20 c16 :: c16:c17:c18:c19:c20 c17 :: c16:c17:c18:c19:c20 c18 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c19 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 c20 :: c16:c17:c18:c19:c20 terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c21 :: c:c1 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c22 :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c23 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c24 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c25 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c26 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c27 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c28 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c29 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 recip :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c30 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c31 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c32 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 nil :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c33 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 a__terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c:c11_34 :: c:c1 hole_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil2_34 :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c2:c3:c4:c53_34 :: c2:c3:c4:c5 hole_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c334_34 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 hole_c9:c10:c11:c125_34 :: c9:c10:c11:c12 hole_c6:c7:c86_34 :: c6:c7:c8 hole_c13:c14:c157_34 :: c13:c14:c15 hole_c16:c17:c18:c19:c208_34 :: c16:c17:c18:c19:c20 gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34 :: Nat -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil gen_c2:c3:c4:c510_34 :: Nat -> c2:c3:c4:c5 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34 :: Nat -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 gen_c9:c10:c11:c1212_34 :: Nat -> c9:c10:c11:c12 gen_c6:c7:c813_34 :: Nat -> c6:c7:c8 gen_c16:c17:c18:c19:c2014_34 :: Nat -> c16:c17:c18:c19:c20 ---------------------------------------- (13) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: A__TERMS, A__SQR, mark, MARK, A__ADD, a__sqr, a__dbl, A__DBL, A__HALF, a__terms, a__add, a__half They will be analysed ascendingly in the following order: A__TERMS = A__SQR mark < A__TERMS A__TERMS = MARK A__TERMS = A__ADD A__TERMS = A__DBL A__TERMS = A__HALF mark < A__SQR A__SQR = MARK A__SQR = A__ADD a__sqr < A__SQR a__dbl < A__SQR A__SQR = A__DBL A__SQR = A__HALF mark < MARK mark < A__ADD mark = a__sqr mark = a__dbl mark < A__DBL mark < A__HALF mark = a__terms mark = a__add mark = a__half MARK = A__ADD MARK = A__DBL MARK = A__HALF A__ADD = A__DBL A__ADD = A__HALF a__sqr = a__dbl a__sqr = a__terms a__sqr = a__add a__sqr = a__half a__dbl = a__terms a__dbl = a__add a__dbl = a__half A__DBL = A__HALF a__terms = a__add a__terms = a__half a__add = a__half ---------------------------------------- (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__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__SQR(z0) -> c5 A__DBL(0') -> c6 A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__DBL(z0) -> c8 A__ADD(0', z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c12 A__FIRST(0', z0) -> c13 A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__FIRST(z0, z1) -> c15 A__HALF(0') -> c16 A__HALF(s(0')) -> c17 A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) A__HALF(z0) -> c20 MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) MARK(0') -> c32 MARK(nil) -> c33 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0') -> 0' a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0', z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0') -> 0' a__half(s(0')) -> 0' a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' mark(nil) -> nil Types: A__TERMS :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c:c1 c :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c:c1 A__SQR :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c2:c3:c4:c5 mark :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil MARK :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c1 :: c:c1 0' :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c2 :: c2:c3:c4:c5 s :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c3 :: c9:c10:c11:c12 -> c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__ADD :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c9:c10:c11:c12 a__sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c4 :: c9:c10:c11:c12 -> c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__DBL :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c6:c7:c8 c5 :: c2:c3:c4:c5 c6 :: c6:c7:c8 c7 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c6:c7:c8 c8 :: c6:c7:c8 c9 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c10 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c11 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c12 :: c9:c10:c11:c12 A__FIRST :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c13:c14:c15 c13 :: c13:c14:c15 cons :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c14 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c13:c14:c15 c15 :: c13:c14:c15 A__HALF :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c16:c17:c18:c19:c20 c16 :: c16:c17:c18:c19:c20 c17 :: c16:c17:c18:c19:c20 c18 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c19 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 c20 :: c16:c17:c18:c19:c20 terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c21 :: c:c1 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c22 :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c23 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c24 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c25 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c26 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c27 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c28 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c29 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 recip :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c30 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c31 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c32 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 nil :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c33 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 a__terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c:c11_34 :: c:c1 hole_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil2_34 :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c2:c3:c4:c53_34 :: c2:c3:c4:c5 hole_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c334_34 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 hole_c9:c10:c11:c125_34 :: c9:c10:c11:c12 hole_c6:c7:c86_34 :: c6:c7:c8 hole_c13:c14:c157_34 :: c13:c14:c15 hole_c16:c17:c18:c19:c208_34 :: c16:c17:c18:c19:c20 gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34 :: Nat -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil gen_c2:c3:c4:c510_34 :: Nat -> c2:c3:c4:c5 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34 :: Nat -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 gen_c9:c10:c11:c1212_34 :: Nat -> c9:c10:c11:c12 gen_c6:c7:c813_34 :: Nat -> c6:c7:c8 gen_c16:c17:c18:c19:c2014_34 :: Nat -> c16:c17:c18:c19:c20 Generator Equations: gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0) <=> 0' gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(x, 1)) <=> s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(x)) gen_c2:c3:c4:c510_34(0) <=> c2 gen_c2:c3:c4:c510_34(+(x, 1)) <=> c3(c9(c32), gen_c2:c3:c4:c510_34(x), c32) gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(0) <=> c32 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(+(x, 1)) <=> c21(c(c2, c32), gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(x)) gen_c9:c10:c11:c1212_34(0) <=> c9(c32) gen_c9:c10:c11:c1212_34(+(x, 1)) <=> c10(gen_c9:c10:c11:c1212_34(x), c32) gen_c6:c7:c813_34(0) <=> c6 gen_c6:c7:c813_34(+(x, 1)) <=> c7(gen_c6:c7:c813_34(x), c32) gen_c16:c17:c18:c19:c2014_34(0) <=> c16 gen_c16:c17:c18:c19:c2014_34(+(x, 1)) <=> c18(gen_c16:c17:c18:c19:c2014_34(x), c32) The following defined symbols remain to be analysed: a__terms, A__TERMS, A__SQR, mark, MARK, A__ADD, a__sqr, a__dbl, A__DBL, A__HALF, a__add, a__half They will be analysed ascendingly in the following order: A__TERMS = A__SQR mark < A__TERMS A__TERMS = MARK A__TERMS = A__ADD A__TERMS = A__DBL A__TERMS = A__HALF mark < A__SQR A__SQR = MARK A__SQR = A__ADD a__sqr < A__SQR a__dbl < A__SQR A__SQR = A__DBL A__SQR = A__HALF mark < MARK mark < A__ADD mark = a__sqr mark = a__dbl mark < A__DBL mark < A__HALF mark = a__terms mark = a__add mark = a__half MARK = A__ADD MARK = A__DBL MARK = A__HALF A__ADD = A__DBL A__ADD = A__HALF a__sqr = a__dbl a__sqr = a__terms a__sqr = a__add a__sqr = a__half a__dbl = a__terms a__dbl = a__add a__dbl = a__half A__DBL = A__HALF a__terms = a__add a__terms = a__half a__add = a__half ---------------------------------------- (15) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n2993292_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n2993292_34), rt in Omega(0) Induction Base: mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0)) ->_R^Omega(0) 0' Induction Step: mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(n2993292_34, 1))) ->_R^Omega(0) s(mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n2993292_34))) ->_IH s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(c2993293_34)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (16) Obligation: Innermost TRS: Rules: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__TERMS(z0) -> c1 A__SQR(0') -> c2 A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__SQR(z0) -> c5 A__DBL(0') -> c6 A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__DBL(z0) -> c8 A__ADD(0', z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c12 A__FIRST(0', z0) -> c13 A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__FIRST(z0, z1) -> c15 A__HALF(0') -> c16 A__HALF(s(0')) -> c17 A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) A__HALF(z0) -> c20 MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) MARK(0') -> c32 MARK(nil) -> c33 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0') -> 0' a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0', z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0') -> 0' a__half(s(0')) -> 0' a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' mark(nil) -> nil Types: A__TERMS :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c:c1 c :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c:c1 A__SQR :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c2:c3:c4:c5 mark :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil MARK :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c1 :: c:c1 0' :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c2 :: c2:c3:c4:c5 s :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c3 :: c9:c10:c11:c12 -> c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__ADD :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c9:c10:c11:c12 a__sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c4 :: c9:c10:c11:c12 -> c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__DBL :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c6:c7:c8 c5 :: c2:c3:c4:c5 c6 :: c6:c7:c8 c7 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c6:c7:c8 c8 :: c6:c7:c8 c9 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c10 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c11 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c12 :: c9:c10:c11:c12 A__FIRST :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c13:c14:c15 c13 :: c13:c14:c15 cons :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c14 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c13:c14:c15 c15 :: c13:c14:c15 A__HALF :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c16:c17:c18:c19:c20 c16 :: c16:c17:c18:c19:c20 c17 :: c16:c17:c18:c19:c20 c18 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c19 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 c20 :: c16:c17:c18:c19:c20 terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c21 :: c:c1 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c22 :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c23 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c24 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c25 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c26 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c27 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c28 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c29 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 recip :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c30 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c31 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c32 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 nil :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c33 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 a__terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c:c11_34 :: c:c1 hole_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil2_34 :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c2:c3:c4:c53_34 :: c2:c3:c4:c5 hole_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c334_34 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 hole_c9:c10:c11:c125_34 :: c9:c10:c11:c12 hole_c6:c7:c86_34 :: c6:c7:c8 hole_c13:c14:c157_34 :: c13:c14:c15 hole_c16:c17:c18:c19:c208_34 :: c16:c17:c18:c19:c20 gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34 :: Nat -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil gen_c2:c3:c4:c510_34 :: Nat -> c2:c3:c4:c5 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34 :: Nat -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 gen_c9:c10:c11:c1212_34 :: Nat -> c9:c10:c11:c12 gen_c6:c7:c813_34 :: Nat -> c6:c7:c8 gen_c16:c17:c18:c19:c2014_34 :: Nat -> c16:c17:c18:c19:c20 Lemmas: mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n2993292_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n2993292_34), rt in Omega(0) Generator Equations: gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0) <=> 0' gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(x, 1)) <=> s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(x)) gen_c2:c3:c4:c510_34(0) <=> c2 gen_c2:c3:c4:c510_34(+(x, 1)) <=> c3(c9(c32), gen_c2:c3:c4:c510_34(x), c32) gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(0) <=> c32 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(+(x, 1)) <=> c21(c(c2, c32), gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(x)) gen_c9:c10:c11:c1212_34(0) <=> c9(c32) gen_c9:c10:c11:c1212_34(+(x, 1)) <=> c10(gen_c9:c10:c11:c1212_34(x), c32) gen_c6:c7:c813_34(0) <=> c6 gen_c6:c7:c813_34(+(x, 1)) <=> c7(gen_c6:c7:c813_34(x), c32) gen_c16:c17:c18:c19:c2014_34(0) <=> c16 gen_c16:c17:c18:c19:c2014_34(+(x, 1)) <=> c18(gen_c16:c17:c18:c19:c2014_34(x), c32) The following defined symbols remain to be analysed: a__dbl, A__TERMS, A__SQR, MARK, A__ADD, a__sqr, A__DBL, A__HALF, a__terms, a__add, a__half They will be analysed ascendingly in the following order: A__TERMS = A__SQR mark < A__TERMS A__TERMS = MARK A__TERMS = A__ADD A__TERMS = A__DBL A__TERMS = A__HALF mark < A__SQR A__SQR = MARK A__SQR = A__ADD a__sqr < A__SQR a__dbl < A__SQR A__SQR = A__DBL A__SQR = A__HALF mark < MARK mark < A__ADD mark = a__sqr mark = a__dbl mark < A__DBL mark < A__HALF mark = a__terms mark = a__add mark = a__half MARK = A__ADD MARK = A__DBL MARK = A__HALF A__ADD = A__DBL A__ADD = A__HALF a__sqr = a__dbl a__sqr = a__terms a__sqr = a__add a__sqr = a__half a__dbl = a__terms a__dbl = a__add a__dbl = a__half A__DBL = A__HALF a__terms = a__add a__terms = a__half a__add = a__half ---------------------------------------- (17) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3012241_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3012241_34)), rt in Omega(0) Induction Base: a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0)) ->_R^Omega(0) 0' Induction Step: a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(n3012241_34, 1))) ->_R^Omega(0) s(s(a__dbl(mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3012241_34))))) ->_L^Omega(0) s(s(a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3012241_34)))) ->_IH s(s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, c3012242_34)))) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (18) Obligation: Innermost TRS: Rules: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__TERMS(z0) -> c1 A__SQR(0') -> c2 A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__SQR(z0) -> c5 A__DBL(0') -> c6 A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__DBL(z0) -> c8 A__ADD(0', z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c12 A__FIRST(0', z0) -> c13 A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__FIRST(z0, z1) -> c15 A__HALF(0') -> c16 A__HALF(s(0')) -> c17 A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) A__HALF(z0) -> c20 MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) MARK(0') -> c32 MARK(nil) -> c33 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0') -> 0' a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0', z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0') -> 0' a__half(s(0')) -> 0' a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' mark(nil) -> nil Types: A__TERMS :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c:c1 c :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c:c1 A__SQR :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c2:c3:c4:c5 mark :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil MARK :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c1 :: c:c1 0' :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c2 :: c2:c3:c4:c5 s :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c3 :: c9:c10:c11:c12 -> c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__ADD :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c9:c10:c11:c12 a__sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c4 :: c9:c10:c11:c12 -> c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__DBL :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c6:c7:c8 c5 :: c2:c3:c4:c5 c6 :: c6:c7:c8 c7 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c6:c7:c8 c8 :: c6:c7:c8 c9 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c10 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c11 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c12 :: c9:c10:c11:c12 A__FIRST :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c13:c14:c15 c13 :: c13:c14:c15 cons :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c14 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c13:c14:c15 c15 :: c13:c14:c15 A__HALF :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c16:c17:c18:c19:c20 c16 :: c16:c17:c18:c19:c20 c17 :: c16:c17:c18:c19:c20 c18 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c19 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 c20 :: c16:c17:c18:c19:c20 terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c21 :: c:c1 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c22 :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c23 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c24 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c25 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c26 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c27 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c28 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c29 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 recip :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c30 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c31 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c32 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 nil :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c33 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 a__terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c:c11_34 :: c:c1 hole_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil2_34 :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c2:c3:c4:c53_34 :: c2:c3:c4:c5 hole_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c334_34 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 hole_c9:c10:c11:c125_34 :: c9:c10:c11:c12 hole_c6:c7:c86_34 :: c6:c7:c8 hole_c13:c14:c157_34 :: c13:c14:c15 hole_c16:c17:c18:c19:c208_34 :: c16:c17:c18:c19:c20 gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34 :: Nat -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil gen_c2:c3:c4:c510_34 :: Nat -> c2:c3:c4:c5 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34 :: Nat -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 gen_c9:c10:c11:c1212_34 :: Nat -> c9:c10:c11:c12 gen_c6:c7:c813_34 :: Nat -> c6:c7:c8 gen_c16:c17:c18:c19:c2014_34 :: Nat -> c16:c17:c18:c19:c20 Lemmas: mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n2993292_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n2993292_34), rt in Omega(0) a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3012241_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3012241_34)), rt in Omega(0) Generator Equations: gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0) <=> 0' gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(x, 1)) <=> s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(x)) gen_c2:c3:c4:c510_34(0) <=> c2 gen_c2:c3:c4:c510_34(+(x, 1)) <=> c3(c9(c32), gen_c2:c3:c4:c510_34(x), c32) gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(0) <=> c32 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(+(x, 1)) <=> c21(c(c2, c32), gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(x)) gen_c9:c10:c11:c1212_34(0) <=> c9(c32) gen_c9:c10:c11:c1212_34(+(x, 1)) <=> c10(gen_c9:c10:c11:c1212_34(x), c32) gen_c6:c7:c813_34(0) <=> c6 gen_c6:c7:c813_34(+(x, 1)) <=> c7(gen_c6:c7:c813_34(x), c32) gen_c16:c17:c18:c19:c2014_34(0) <=> c16 gen_c16:c17:c18:c19:c2014_34(+(x, 1)) <=> c18(gen_c16:c17:c18:c19:c2014_34(x), c32) The following defined symbols remain to be analysed: a__half, A__TERMS, A__SQR, mark, MARK, A__ADD, a__sqr, A__DBL, A__HALF, a__terms, a__add They will be analysed ascendingly in the following order: A__TERMS = A__SQR mark < A__TERMS A__TERMS = MARK A__TERMS = A__ADD A__TERMS = A__DBL A__TERMS = A__HALF mark < A__SQR A__SQR = MARK A__SQR = A__ADD a__sqr < A__SQR a__dbl < A__SQR A__SQR = A__DBL A__SQR = A__HALF mark < MARK mark < A__ADD mark = a__sqr mark = a__dbl mark < A__DBL mark < A__HALF mark = a__terms mark = a__add mark = a__half MARK = A__ADD MARK = A__DBL MARK = A__HALF A__ADD = A__DBL A__ADD = A__HALF a__sqr = a__dbl a__sqr = a__terms a__sqr = a__add a__sqr = a__half a__dbl = a__terms a__dbl = a__add a__dbl = a__half A__DBL = A__HALF a__terms = a__add a__terms = a__half a__add = a__half ---------------------------------------- (19) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__half(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3013179_34))) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3013179_34), rt in Omega(0) Induction Base: a__half(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, 0))) ->_R^Omega(0) 0' Induction Step: a__half(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, +(n3013179_34, 1)))) ->_R^Omega(0) s(a__half(mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3013179_34))))) ->_L^Omega(0) s(a__half(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3013179_34)))) ->_IH s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(c3013180_34)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (20) Obligation: Innermost TRS: Rules: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__TERMS(z0) -> c1 A__SQR(0') -> c2 A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__SQR(z0) -> c5 A__DBL(0') -> c6 A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__DBL(z0) -> c8 A__ADD(0', z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c12 A__FIRST(0', z0) -> c13 A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__FIRST(z0, z1) -> c15 A__HALF(0') -> c16 A__HALF(s(0')) -> c17 A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) A__HALF(z0) -> c20 MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) MARK(0') -> c32 MARK(nil) -> c33 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0') -> 0' a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0', z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0') -> 0' a__half(s(0')) -> 0' a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' mark(nil) -> nil Types: A__TERMS :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c:c1 c :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c:c1 A__SQR :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c2:c3:c4:c5 mark :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil MARK :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c1 :: c:c1 0' :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c2 :: c2:c3:c4:c5 s :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c3 :: c9:c10:c11:c12 -> c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__ADD :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c9:c10:c11:c12 a__sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c4 :: c9:c10:c11:c12 -> c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__DBL :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c6:c7:c8 c5 :: c2:c3:c4:c5 c6 :: c6:c7:c8 c7 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c6:c7:c8 c8 :: c6:c7:c8 c9 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c10 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c11 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c12 :: c9:c10:c11:c12 A__FIRST :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c13:c14:c15 c13 :: c13:c14:c15 cons :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c14 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c13:c14:c15 c15 :: c13:c14:c15 A__HALF :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c16:c17:c18:c19:c20 c16 :: c16:c17:c18:c19:c20 c17 :: c16:c17:c18:c19:c20 c18 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c19 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 c20 :: c16:c17:c18:c19:c20 terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c21 :: c:c1 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c22 :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c23 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c24 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c25 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c26 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c27 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c28 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c29 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 recip :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c30 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c31 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c32 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 nil :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c33 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 a__terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c:c11_34 :: c:c1 hole_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil2_34 :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c2:c3:c4:c53_34 :: c2:c3:c4:c5 hole_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c334_34 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 hole_c9:c10:c11:c125_34 :: c9:c10:c11:c12 hole_c6:c7:c86_34 :: c6:c7:c8 hole_c13:c14:c157_34 :: c13:c14:c15 hole_c16:c17:c18:c19:c208_34 :: c16:c17:c18:c19:c20 gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34 :: Nat -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil gen_c2:c3:c4:c510_34 :: Nat -> c2:c3:c4:c5 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34 :: Nat -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 gen_c9:c10:c11:c1212_34 :: Nat -> c9:c10:c11:c12 gen_c6:c7:c813_34 :: Nat -> c6:c7:c8 gen_c16:c17:c18:c19:c2014_34 :: Nat -> c16:c17:c18:c19:c20 Lemmas: mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n2993292_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n2993292_34), rt in Omega(0) a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3012241_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3012241_34)), rt in Omega(0) a__half(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3013179_34))) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3013179_34), rt in Omega(0) Generator Equations: gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0) <=> 0' gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(x, 1)) <=> s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(x)) gen_c2:c3:c4:c510_34(0) <=> c2 gen_c2:c3:c4:c510_34(+(x, 1)) <=> c3(c9(c32), gen_c2:c3:c4:c510_34(x), c32) gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(0) <=> c32 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(+(x, 1)) <=> c21(c(c2, c32), gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(x)) gen_c9:c10:c11:c1212_34(0) <=> c9(c32) gen_c9:c10:c11:c1212_34(+(x, 1)) <=> c10(gen_c9:c10:c11:c1212_34(x), c32) gen_c6:c7:c813_34(0) <=> c6 gen_c6:c7:c813_34(+(x, 1)) <=> c7(gen_c6:c7:c813_34(x), c32) gen_c16:c17:c18:c19:c2014_34(0) <=> c16 gen_c16:c17:c18:c19:c2014_34(+(x, 1)) <=> c18(gen_c16:c17:c18:c19:c2014_34(x), c32) The following defined symbols remain to be analysed: a__terms, A__TERMS, A__SQR, mark, MARK, A__ADD, a__sqr, a__dbl, A__DBL, A__HALF, a__add They will be analysed ascendingly in the following order: A__TERMS = A__SQR mark < A__TERMS A__TERMS = MARK A__TERMS = A__ADD A__TERMS = A__DBL A__TERMS = A__HALF mark < A__SQR A__SQR = MARK A__SQR = A__ADD a__sqr < A__SQR a__dbl < A__SQR A__SQR = A__DBL A__SQR = A__HALF mark < MARK mark < A__ADD mark = a__sqr mark = a__dbl mark < A__DBL mark < A__HALF mark = a__terms mark = a__add mark = a__half MARK = A__ADD MARK = A__DBL MARK = A__HALF A__ADD = A__DBL A__ADD = A__HALF a__sqr = a__dbl a__sqr = a__terms a__sqr = a__add a__sqr = a__half a__dbl = a__terms a__dbl = a__add a__dbl = a__half A__DBL = A__HALF a__terms = a__add a__terms = a__half a__add = a__half ---------------------------------------- (21) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__sqr(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3016723_34)) -> *15_34, rt in Omega(0) Induction Base: a__sqr(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0)) Induction Step: a__sqr(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(n3016723_34, 1))) ->_R^Omega(0) s(a__add(a__sqr(mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3016723_34))), a__dbl(mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3016723_34))))) ->_L^Omega(0) s(a__add(a__sqr(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3016723_34)), a__dbl(mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3016723_34))))) ->_IH s(a__add(*15_34, a__dbl(mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3016723_34))))) ->_L^Omega(0) s(a__add(*15_34, a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3016723_34)))) ->_L^Omega(0) s(a__add(*15_34, gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3016723_34)))) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (22) Obligation: Innermost TRS: Rules: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__TERMS(z0) -> c1 A__SQR(0') -> c2 A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__SQR(z0) -> c5 A__DBL(0') -> c6 A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__DBL(z0) -> c8 A__ADD(0', z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c12 A__FIRST(0', z0) -> c13 A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__FIRST(z0, z1) -> c15 A__HALF(0') -> c16 A__HALF(s(0')) -> c17 A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) A__HALF(z0) -> c20 MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) MARK(0') -> c32 MARK(nil) -> c33 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0') -> 0' a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0', z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0') -> 0' a__half(s(0')) -> 0' a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' mark(nil) -> nil Types: A__TERMS :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c:c1 c :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c:c1 A__SQR :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c2:c3:c4:c5 mark :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil MARK :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c1 :: c:c1 0' :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c2 :: c2:c3:c4:c5 s :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c3 :: c9:c10:c11:c12 -> c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__ADD :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c9:c10:c11:c12 a__sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c4 :: c9:c10:c11:c12 -> c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__DBL :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c6:c7:c8 c5 :: c2:c3:c4:c5 c6 :: c6:c7:c8 c7 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c6:c7:c8 c8 :: c6:c7:c8 c9 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c10 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c11 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c12 :: c9:c10:c11:c12 A__FIRST :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c13:c14:c15 c13 :: c13:c14:c15 cons :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c14 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c13:c14:c15 c15 :: c13:c14:c15 A__HALF :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c16:c17:c18:c19:c20 c16 :: c16:c17:c18:c19:c20 c17 :: c16:c17:c18:c19:c20 c18 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c19 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 c20 :: c16:c17:c18:c19:c20 terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c21 :: c:c1 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c22 :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c23 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c24 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c25 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c26 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c27 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c28 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c29 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 recip :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c30 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c31 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c32 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 nil :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c33 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 a__terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c:c11_34 :: c:c1 hole_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil2_34 :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c2:c3:c4:c53_34 :: c2:c3:c4:c5 hole_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c334_34 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 hole_c9:c10:c11:c125_34 :: c9:c10:c11:c12 hole_c6:c7:c86_34 :: c6:c7:c8 hole_c13:c14:c157_34 :: c13:c14:c15 hole_c16:c17:c18:c19:c208_34 :: c16:c17:c18:c19:c20 gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34 :: Nat -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil gen_c2:c3:c4:c510_34 :: Nat -> c2:c3:c4:c5 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34 :: Nat -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 gen_c9:c10:c11:c1212_34 :: Nat -> c9:c10:c11:c12 gen_c6:c7:c813_34 :: Nat -> c6:c7:c8 gen_c16:c17:c18:c19:c2014_34 :: Nat -> c16:c17:c18:c19:c20 Lemmas: mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n2993292_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n2993292_34), rt in Omega(0) a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3012241_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3012241_34)), rt in Omega(0) a__half(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3013179_34))) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3013179_34), rt in Omega(0) a__sqr(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3016723_34)) -> *15_34, rt in Omega(0) Generator Equations: gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0) <=> 0' gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(x, 1)) <=> s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(x)) gen_c2:c3:c4:c510_34(0) <=> c2 gen_c2:c3:c4:c510_34(+(x, 1)) <=> c3(c9(c32), gen_c2:c3:c4:c510_34(x), c32) gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(0) <=> c32 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(+(x, 1)) <=> c21(c(c2, c32), gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(x)) gen_c9:c10:c11:c1212_34(0) <=> c9(c32) gen_c9:c10:c11:c1212_34(+(x, 1)) <=> c10(gen_c9:c10:c11:c1212_34(x), c32) gen_c6:c7:c813_34(0) <=> c6 gen_c6:c7:c813_34(+(x, 1)) <=> c7(gen_c6:c7:c813_34(x), c32) gen_c16:c17:c18:c19:c2014_34(0) <=> c16 gen_c16:c17:c18:c19:c2014_34(+(x, 1)) <=> c18(gen_c16:c17:c18:c19:c2014_34(x), c32) The following defined symbols remain to be analysed: a__add, A__TERMS, A__SQR, mark, MARK, A__ADD, a__dbl, A__DBL, A__HALF, a__terms, a__half They will be analysed ascendingly in the following order: A__TERMS = A__SQR mark < A__TERMS A__TERMS = MARK A__TERMS = A__ADD A__TERMS = A__DBL A__TERMS = A__HALF mark < A__SQR A__SQR = MARK A__SQR = A__ADD a__sqr < A__SQR a__dbl < A__SQR A__SQR = A__DBL A__SQR = A__HALF mark < MARK mark < A__ADD mark = a__sqr mark = a__dbl mark < A__DBL mark < A__HALF mark = a__terms mark = a__add mark = a__half MARK = A__ADD MARK = A__DBL MARK = A__HALF A__ADD = A__DBL A__ADD = A__HALF a__sqr = a__dbl a__sqr = a__terms a__sqr = a__add a__sqr = a__half a__dbl = a__terms a__dbl = a__add a__dbl = a__half A__DBL = A__HALF a__terms = a__add a__terms = a__half a__add = a__half ---------------------------------------- (23) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__add(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3021342_34), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(n3021342_34, b)), rt in Omega(0) Induction Base: a__add(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)) ->_R^Omega(0) mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)) ->_L^Omega(0) gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b) Induction Step: a__add(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(n3021342_34, 1)), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)) ->_R^Omega(0) s(a__add(mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3021342_34)), mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)))) ->_L^Omega(0) s(a__add(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3021342_34), mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)))) ->_L^Omega(0) s(a__add(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3021342_34), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b))) ->_IH s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(b, c3021343_34))) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (24) Obligation: Innermost TRS: Rules: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__TERMS(z0) -> c1 A__SQR(0') -> c2 A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__SQR(z0) -> c5 A__DBL(0') -> c6 A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__DBL(z0) -> c8 A__ADD(0', z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c12 A__FIRST(0', z0) -> c13 A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__FIRST(z0, z1) -> c15 A__HALF(0') -> c16 A__HALF(s(0')) -> c17 A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) A__HALF(z0) -> c20 MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) MARK(0') -> c32 MARK(nil) -> c33 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0') -> 0' a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0', z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0') -> 0' a__half(s(0')) -> 0' a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' mark(nil) -> nil Types: A__TERMS :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c:c1 c :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c:c1 A__SQR :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c2:c3:c4:c5 mark :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil MARK :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c1 :: c:c1 0' :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c2 :: c2:c3:c4:c5 s :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c3 :: c9:c10:c11:c12 -> c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__ADD :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c9:c10:c11:c12 a__sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c4 :: c9:c10:c11:c12 -> c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__DBL :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c6:c7:c8 c5 :: c2:c3:c4:c5 c6 :: c6:c7:c8 c7 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c6:c7:c8 c8 :: c6:c7:c8 c9 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c10 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c11 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c12 :: c9:c10:c11:c12 A__FIRST :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c13:c14:c15 c13 :: c13:c14:c15 cons :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c14 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c13:c14:c15 c15 :: c13:c14:c15 A__HALF :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c16:c17:c18:c19:c20 c16 :: c16:c17:c18:c19:c20 c17 :: c16:c17:c18:c19:c20 c18 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c19 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 c20 :: c16:c17:c18:c19:c20 terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c21 :: c:c1 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c22 :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c23 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c24 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c25 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c26 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c27 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c28 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c29 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 recip :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c30 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c31 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c32 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 nil :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c33 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 a__terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c:c11_34 :: c:c1 hole_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil2_34 :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c2:c3:c4:c53_34 :: c2:c3:c4:c5 hole_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c334_34 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 hole_c9:c10:c11:c125_34 :: c9:c10:c11:c12 hole_c6:c7:c86_34 :: c6:c7:c8 hole_c13:c14:c157_34 :: c13:c14:c15 hole_c16:c17:c18:c19:c208_34 :: c16:c17:c18:c19:c20 gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34 :: Nat -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil gen_c2:c3:c4:c510_34 :: Nat -> c2:c3:c4:c5 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34 :: Nat -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 gen_c9:c10:c11:c1212_34 :: Nat -> c9:c10:c11:c12 gen_c6:c7:c813_34 :: Nat -> c6:c7:c8 gen_c16:c17:c18:c19:c2014_34 :: Nat -> c16:c17:c18:c19:c20 Lemmas: mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n2993292_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n2993292_34), rt in Omega(0) a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3012241_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3012241_34)), rt in Omega(0) a__half(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3013179_34))) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3013179_34), rt in Omega(0) a__sqr(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3016723_34)) -> *15_34, rt in Omega(0) a__add(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3021342_34), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(n3021342_34, b)), rt in Omega(0) Generator Equations: gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0) <=> 0' gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(x, 1)) <=> s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(x)) gen_c2:c3:c4:c510_34(0) <=> c2 gen_c2:c3:c4:c510_34(+(x, 1)) <=> c3(c9(c32), gen_c2:c3:c4:c510_34(x), c32) gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(0) <=> c32 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(+(x, 1)) <=> c21(c(c2, c32), gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(x)) gen_c9:c10:c11:c1212_34(0) <=> c9(c32) gen_c9:c10:c11:c1212_34(+(x, 1)) <=> c10(gen_c9:c10:c11:c1212_34(x), c32) gen_c6:c7:c813_34(0) <=> c6 gen_c6:c7:c813_34(+(x, 1)) <=> c7(gen_c6:c7:c813_34(x), c32) gen_c16:c17:c18:c19:c2014_34(0) <=> c16 gen_c16:c17:c18:c19:c2014_34(+(x, 1)) <=> c18(gen_c16:c17:c18:c19:c2014_34(x), c32) The following defined symbols remain to be analysed: mark, A__TERMS, A__SQR, MARK, A__ADD, a__sqr, a__dbl, A__DBL, A__HALF, a__terms, a__half They will be analysed ascendingly in the following order: A__TERMS = A__SQR mark < A__TERMS A__TERMS = MARK A__TERMS = A__ADD A__TERMS = A__DBL A__TERMS = A__HALF mark < A__SQR A__SQR = MARK A__SQR = A__ADD a__sqr < A__SQR a__dbl < A__SQR A__SQR = A__DBL A__SQR = A__HALF mark < MARK mark < A__ADD mark = a__sqr mark = a__dbl mark < A__DBL mark < A__HALF mark = a__terms mark = a__add mark = a__half MARK = A__ADD MARK = A__DBL MARK = A__HALF A__ADD = A__DBL A__ADD = A__HALF a__sqr = a__dbl a__sqr = a__terms a__sqr = a__add a__sqr = a__half a__dbl = a__terms a__dbl = a__add a__dbl = a__half A__DBL = A__HALF a__terms = a__add a__terms = a__half a__add = a__half ---------------------------------------- (25) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3025630_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3025630_34), rt in Omega(0) Induction Base: mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0)) ->_R^Omega(0) 0' Induction Step: mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(n3025630_34, 1))) ->_R^Omega(0) s(mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3025630_34))) ->_IH s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(c3025631_34)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (26) Obligation: Innermost TRS: Rules: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__TERMS(z0) -> c1 A__SQR(0') -> c2 A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__SQR(z0) -> c5 A__DBL(0') -> c6 A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__DBL(z0) -> c8 A__ADD(0', z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c12 A__FIRST(0', z0) -> c13 A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__FIRST(z0, z1) -> c15 A__HALF(0') -> c16 A__HALF(s(0')) -> c17 A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) A__HALF(z0) -> c20 MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) MARK(0') -> c32 MARK(nil) -> c33 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0') -> 0' a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0', z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0') -> 0' a__half(s(0')) -> 0' a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' mark(nil) -> nil Types: A__TERMS :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c:c1 c :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c:c1 A__SQR :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c2:c3:c4:c5 mark :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil MARK :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c1 :: c:c1 0' :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c2 :: c2:c3:c4:c5 s :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c3 :: c9:c10:c11:c12 -> c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__ADD :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c9:c10:c11:c12 a__sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c4 :: c9:c10:c11:c12 -> c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__DBL :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c6:c7:c8 c5 :: c2:c3:c4:c5 c6 :: c6:c7:c8 c7 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c6:c7:c8 c8 :: c6:c7:c8 c9 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c10 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c11 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c12 :: c9:c10:c11:c12 A__FIRST :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c13:c14:c15 c13 :: c13:c14:c15 cons :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c14 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c13:c14:c15 c15 :: c13:c14:c15 A__HALF :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c16:c17:c18:c19:c20 c16 :: c16:c17:c18:c19:c20 c17 :: c16:c17:c18:c19:c20 c18 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c19 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 c20 :: c16:c17:c18:c19:c20 terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c21 :: c:c1 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c22 :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c23 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c24 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c25 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c26 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c27 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c28 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c29 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 recip :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c30 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c31 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c32 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 nil :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c33 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 a__terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c:c11_34 :: c:c1 hole_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil2_34 :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c2:c3:c4:c53_34 :: c2:c3:c4:c5 hole_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c334_34 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 hole_c9:c10:c11:c125_34 :: c9:c10:c11:c12 hole_c6:c7:c86_34 :: c6:c7:c8 hole_c13:c14:c157_34 :: c13:c14:c15 hole_c16:c17:c18:c19:c208_34 :: c16:c17:c18:c19:c20 gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34 :: Nat -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil gen_c2:c3:c4:c510_34 :: Nat -> c2:c3:c4:c5 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34 :: Nat -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 gen_c9:c10:c11:c1212_34 :: Nat -> c9:c10:c11:c12 gen_c6:c7:c813_34 :: Nat -> c6:c7:c8 gen_c16:c17:c18:c19:c2014_34 :: Nat -> c16:c17:c18:c19:c20 Lemmas: mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3025630_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3025630_34), rt in Omega(0) a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3012241_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3012241_34)), rt in Omega(0) a__half(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3013179_34))) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3013179_34), rt in Omega(0) a__sqr(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3016723_34)) -> *15_34, rt in Omega(0) a__add(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3021342_34), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(n3021342_34, b)), rt in Omega(0) Generator Equations: gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0) <=> 0' gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(x, 1)) <=> s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(x)) gen_c2:c3:c4:c510_34(0) <=> c2 gen_c2:c3:c4:c510_34(+(x, 1)) <=> c3(c9(c32), gen_c2:c3:c4:c510_34(x), c32) gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(0) <=> c32 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(+(x, 1)) <=> c21(c(c2, c32), gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(x)) gen_c9:c10:c11:c1212_34(0) <=> c9(c32) gen_c9:c10:c11:c1212_34(+(x, 1)) <=> c10(gen_c9:c10:c11:c1212_34(x), c32) gen_c6:c7:c813_34(0) <=> c6 gen_c6:c7:c813_34(+(x, 1)) <=> c7(gen_c6:c7:c813_34(x), c32) gen_c16:c17:c18:c19:c2014_34(0) <=> c16 gen_c16:c17:c18:c19:c2014_34(+(x, 1)) <=> c18(gen_c16:c17:c18:c19:c2014_34(x), c32) The following defined symbols remain to be analysed: a__dbl, A__TERMS, A__SQR, MARK, A__ADD, a__sqr, A__DBL, A__HALF, a__terms, a__half They will be analysed ascendingly in the following order: A__TERMS = A__SQR mark < A__TERMS A__TERMS = MARK A__TERMS = A__ADD A__TERMS = A__DBL A__TERMS = A__HALF mark < A__SQR A__SQR = MARK A__SQR = A__ADD a__sqr < A__SQR a__dbl < A__SQR A__SQR = A__DBL A__SQR = A__HALF mark < MARK mark < A__ADD mark = a__sqr mark = a__dbl mark < A__DBL mark < A__HALF mark = a__terms mark = a__add mark = a__half MARK = A__ADD MARK = A__DBL MARK = A__HALF A__ADD = A__DBL A__ADD = A__HALF a__sqr = a__dbl a__sqr = a__terms a__sqr = a__add a__sqr = a__half a__dbl = a__terms a__dbl = a__add a__dbl = a__half A__DBL = A__HALF a__terms = a__add a__terms = a__half a__add = a__half ---------------------------------------- (27) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3044649_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3044649_34)), rt in Omega(0) Induction Base: a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0)) ->_R^Omega(0) 0' Induction Step: a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(n3044649_34, 1))) ->_R^Omega(0) s(s(a__dbl(mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3044649_34))))) ->_L^Omega(0) s(s(a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3044649_34)))) ->_IH s(s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, c3044650_34)))) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (28) Obligation: Innermost TRS: Rules: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__TERMS(z0) -> c1 A__SQR(0') -> c2 A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__SQR(z0) -> c5 A__DBL(0') -> c6 A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__DBL(z0) -> c8 A__ADD(0', z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c12 A__FIRST(0', z0) -> c13 A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__FIRST(z0, z1) -> c15 A__HALF(0') -> c16 A__HALF(s(0')) -> c17 A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) A__HALF(z0) -> c20 MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) MARK(0') -> c32 MARK(nil) -> c33 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0') -> 0' a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0', z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0') -> 0' a__half(s(0')) -> 0' a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' mark(nil) -> nil Types: A__TERMS :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c:c1 c :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c:c1 A__SQR :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c2:c3:c4:c5 mark :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil MARK :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c1 :: c:c1 0' :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c2 :: c2:c3:c4:c5 s :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c3 :: c9:c10:c11:c12 -> c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__ADD :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c9:c10:c11:c12 a__sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c4 :: c9:c10:c11:c12 -> c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__DBL :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c6:c7:c8 c5 :: c2:c3:c4:c5 c6 :: c6:c7:c8 c7 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c6:c7:c8 c8 :: c6:c7:c8 c9 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c10 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c11 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c12 :: c9:c10:c11:c12 A__FIRST :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c13:c14:c15 c13 :: c13:c14:c15 cons :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c14 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c13:c14:c15 c15 :: c13:c14:c15 A__HALF :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c16:c17:c18:c19:c20 c16 :: c16:c17:c18:c19:c20 c17 :: c16:c17:c18:c19:c20 c18 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c19 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 c20 :: c16:c17:c18:c19:c20 terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c21 :: c:c1 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c22 :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c23 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c24 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c25 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c26 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c27 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c28 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c29 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 recip :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c30 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c31 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c32 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 nil :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c33 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 a__terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c:c11_34 :: c:c1 hole_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil2_34 :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c2:c3:c4:c53_34 :: c2:c3:c4:c5 hole_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c334_34 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 hole_c9:c10:c11:c125_34 :: c9:c10:c11:c12 hole_c6:c7:c86_34 :: c6:c7:c8 hole_c13:c14:c157_34 :: c13:c14:c15 hole_c16:c17:c18:c19:c208_34 :: c16:c17:c18:c19:c20 gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34 :: Nat -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil gen_c2:c3:c4:c510_34 :: Nat -> c2:c3:c4:c5 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34 :: Nat -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 gen_c9:c10:c11:c1212_34 :: Nat -> c9:c10:c11:c12 gen_c6:c7:c813_34 :: Nat -> c6:c7:c8 gen_c16:c17:c18:c19:c2014_34 :: Nat -> c16:c17:c18:c19:c20 Lemmas: mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3025630_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3025630_34), rt in Omega(0) a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3044649_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3044649_34)), rt in Omega(0) a__half(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3013179_34))) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3013179_34), rt in Omega(0) a__sqr(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3016723_34)) -> *15_34, rt in Omega(0) a__add(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3021342_34), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(n3021342_34, b)), rt in Omega(0) Generator Equations: gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0) <=> 0' gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(x, 1)) <=> s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(x)) gen_c2:c3:c4:c510_34(0) <=> c2 gen_c2:c3:c4:c510_34(+(x, 1)) <=> c3(c9(c32), gen_c2:c3:c4:c510_34(x), c32) gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(0) <=> c32 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(+(x, 1)) <=> c21(c(c2, c32), gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(x)) gen_c9:c10:c11:c1212_34(0) <=> c9(c32) gen_c9:c10:c11:c1212_34(+(x, 1)) <=> c10(gen_c9:c10:c11:c1212_34(x), c32) gen_c6:c7:c813_34(0) <=> c6 gen_c6:c7:c813_34(+(x, 1)) <=> c7(gen_c6:c7:c813_34(x), c32) gen_c16:c17:c18:c19:c2014_34(0) <=> c16 gen_c16:c17:c18:c19:c2014_34(+(x, 1)) <=> c18(gen_c16:c17:c18:c19:c2014_34(x), c32) The following defined symbols remain to be analysed: a__terms, A__TERMS, A__SQR, MARK, A__ADD, a__sqr, A__DBL, A__HALF, a__half They will be analysed ascendingly in the following order: A__TERMS = A__SQR mark < A__TERMS A__TERMS = MARK A__TERMS = A__ADD A__TERMS = A__DBL A__TERMS = A__HALF mark < A__SQR A__SQR = MARK A__SQR = A__ADD a__sqr < A__SQR a__dbl < A__SQR A__SQR = A__DBL A__SQR = A__HALF mark < MARK mark < A__ADD mark = a__sqr mark = a__dbl mark < A__DBL mark < A__HALF mark = a__terms mark = a__add mark = a__half MARK = A__ADD MARK = A__DBL MARK = A__HALF A__ADD = A__DBL A__ADD = A__HALF a__sqr = a__dbl a__sqr = a__terms a__sqr = a__add a__sqr = a__half a__dbl = a__terms a__dbl = a__add a__dbl = a__half A__DBL = A__HALF a__terms = a__add a__terms = a__half a__add = a__half ---------------------------------------- (29) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__half(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3049071_34))) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3049071_34), rt in Omega(0) Induction Base: a__half(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, 0))) ->_R^Omega(0) 0' Induction Step: a__half(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, +(n3049071_34, 1)))) ->_R^Omega(0) s(a__half(mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3049071_34))))) ->_L^Omega(0) s(a__half(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3049071_34)))) ->_IH s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(c3049072_34)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (30) 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__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__SQR(z0) -> c5 A__DBL(0') -> c6 A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__DBL(z0) -> c8 A__ADD(0', z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c12 A__FIRST(0', z0) -> c13 A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__FIRST(z0, z1) -> c15 A__HALF(0') -> c16 A__HALF(s(0')) -> c17 A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) A__HALF(z0) -> c20 MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) MARK(0') -> c32 MARK(nil) -> c33 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0') -> 0' a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0', z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0') -> 0' a__half(s(0')) -> 0' a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' mark(nil) -> nil Types: A__TERMS :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c:c1 c :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c:c1 A__SQR :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c2:c3:c4:c5 mark :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil MARK :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c1 :: c:c1 0' :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c2 :: c2:c3:c4:c5 s :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c3 :: c9:c10:c11:c12 -> c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__ADD :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c9:c10:c11:c12 a__sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c4 :: c9:c10:c11:c12 -> c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__DBL :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c6:c7:c8 c5 :: c2:c3:c4:c5 c6 :: c6:c7:c8 c7 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c6:c7:c8 c8 :: c6:c7:c8 c9 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c10 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c11 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c12 :: c9:c10:c11:c12 A__FIRST :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c13:c14:c15 c13 :: c13:c14:c15 cons :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c14 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c13:c14:c15 c15 :: c13:c14:c15 A__HALF :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c16:c17:c18:c19:c20 c16 :: c16:c17:c18:c19:c20 c17 :: c16:c17:c18:c19:c20 c18 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c19 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 c20 :: c16:c17:c18:c19:c20 terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c21 :: c:c1 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c22 :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c23 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c24 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c25 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c26 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c27 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c28 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c29 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 recip :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c30 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c31 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c32 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 nil :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c33 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 a__terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c:c11_34 :: c:c1 hole_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil2_34 :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c2:c3:c4:c53_34 :: c2:c3:c4:c5 hole_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c334_34 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 hole_c9:c10:c11:c125_34 :: c9:c10:c11:c12 hole_c6:c7:c86_34 :: c6:c7:c8 hole_c13:c14:c157_34 :: c13:c14:c15 hole_c16:c17:c18:c19:c208_34 :: c16:c17:c18:c19:c20 gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34 :: Nat -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil gen_c2:c3:c4:c510_34 :: Nat -> c2:c3:c4:c5 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34 :: Nat -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 gen_c9:c10:c11:c1212_34 :: Nat -> c9:c10:c11:c12 gen_c6:c7:c813_34 :: Nat -> c6:c7:c8 gen_c16:c17:c18:c19:c2014_34 :: Nat -> c16:c17:c18:c19:c20 Lemmas: mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3025630_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3025630_34), rt in Omega(0) a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3044649_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3044649_34)), rt in Omega(0) a__half(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3049071_34))) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3049071_34), rt in Omega(0) a__sqr(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3016723_34)) -> *15_34, rt in Omega(0) a__add(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3021342_34), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(n3021342_34, b)), rt in Omega(0) Generator Equations: gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0) <=> 0' gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(x, 1)) <=> s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(x)) gen_c2:c3:c4:c510_34(0) <=> c2 gen_c2:c3:c4:c510_34(+(x, 1)) <=> c3(c9(c32), gen_c2:c3:c4:c510_34(x), c32) gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(0) <=> c32 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(+(x, 1)) <=> c21(c(c2, c32), gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(x)) gen_c9:c10:c11:c1212_34(0) <=> c9(c32) gen_c9:c10:c11:c1212_34(+(x, 1)) <=> c10(gen_c9:c10:c11:c1212_34(x), c32) gen_c6:c7:c813_34(0) <=> c6 gen_c6:c7:c813_34(+(x, 1)) <=> c7(gen_c6:c7:c813_34(x), c32) gen_c16:c17:c18:c19:c2014_34(0) <=> c16 gen_c16:c17:c18:c19:c2014_34(+(x, 1)) <=> c18(gen_c16:c17:c18:c19:c2014_34(x), c32) The following defined symbols remain to be analysed: a__sqr, A__TERMS, A__SQR, MARK, A__ADD, A__DBL, A__HALF They will be analysed ascendingly in the following order: A__TERMS = A__SQR mark < A__TERMS A__TERMS = MARK A__TERMS = A__ADD A__TERMS = A__DBL A__TERMS = A__HALF mark < A__SQR A__SQR = MARK A__SQR = A__ADD a__sqr < A__SQR a__dbl < A__SQR A__SQR = A__DBL A__SQR = A__HALF mark < MARK mark < A__ADD mark = a__sqr mark = a__dbl mark < A__DBL mark < A__HALF mark = a__terms mark = a__add mark = a__half MARK = A__ADD MARK = A__DBL MARK = A__HALF A__ADD = A__DBL A__ADD = A__HALF a__sqr = a__dbl a__sqr = a__terms a__sqr = a__add a__sqr = a__half a__dbl = a__terms a__dbl = a__add a__dbl = a__half A__DBL = A__HALF a__terms = a__add a__terms = a__half a__add = a__half ---------------------------------------- (31) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__sqr(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3050242_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(n3050242_34, n3050242_34)), rt in Omega(0) Induction Base: a__sqr(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0)) ->_R^Omega(0) 0' Induction Step: a__sqr(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(n3050242_34, 1))) ->_R^Omega(0) s(a__add(a__sqr(mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3050242_34))), a__dbl(mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3050242_34))))) ->_L^Omega(0) s(a__add(a__sqr(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3050242_34)), a__dbl(mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3050242_34))))) ->_IH s(a__add(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(c3050243_34, c3050243_34)), a__dbl(mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3050242_34))))) ->_L^Omega(0) s(a__add(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(n3050242_34, n3050242_34)), a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3050242_34)))) ->_L^Omega(0) s(a__add(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(n3050242_34, n3050242_34)), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3050242_34)))) ->_L^Omega(0) s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(*(n3050242_34, n3050242_34), *(2, n3050242_34)))) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (32) 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__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__SQR(z0) -> c5 A__DBL(0') -> c6 A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__DBL(z0) -> c8 A__ADD(0', z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c12 A__FIRST(0', z0) -> c13 A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__FIRST(z0, z1) -> c15 A__HALF(0') -> c16 A__HALF(s(0')) -> c17 A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) A__HALF(z0) -> c20 MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) MARK(0') -> c32 MARK(nil) -> c33 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0') -> 0' a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0', z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0') -> 0' a__half(s(0')) -> 0' a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' mark(nil) -> nil Types: A__TERMS :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c:c1 c :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c:c1 A__SQR :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c2:c3:c4:c5 mark :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil MARK :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c1 :: c:c1 0' :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c2 :: c2:c3:c4:c5 s :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c3 :: c9:c10:c11:c12 -> c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__ADD :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c9:c10:c11:c12 a__sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c4 :: c9:c10:c11:c12 -> c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__DBL :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c6:c7:c8 c5 :: c2:c3:c4:c5 c6 :: c6:c7:c8 c7 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c6:c7:c8 c8 :: c6:c7:c8 c9 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c10 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c11 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c12 :: c9:c10:c11:c12 A__FIRST :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c13:c14:c15 c13 :: c13:c14:c15 cons :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c14 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c13:c14:c15 c15 :: c13:c14:c15 A__HALF :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c16:c17:c18:c19:c20 c16 :: c16:c17:c18:c19:c20 c17 :: c16:c17:c18:c19:c20 c18 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c19 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 c20 :: c16:c17:c18:c19:c20 terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c21 :: c:c1 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c22 :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c23 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c24 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c25 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c26 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c27 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c28 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c29 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 recip :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c30 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c31 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c32 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 nil :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c33 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 a__terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c:c11_34 :: c:c1 hole_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil2_34 :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c2:c3:c4:c53_34 :: c2:c3:c4:c5 hole_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c334_34 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 hole_c9:c10:c11:c125_34 :: c9:c10:c11:c12 hole_c6:c7:c86_34 :: c6:c7:c8 hole_c13:c14:c157_34 :: c13:c14:c15 hole_c16:c17:c18:c19:c208_34 :: c16:c17:c18:c19:c20 gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34 :: Nat -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil gen_c2:c3:c4:c510_34 :: Nat -> c2:c3:c4:c5 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34 :: Nat -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 gen_c9:c10:c11:c1212_34 :: Nat -> c9:c10:c11:c12 gen_c6:c7:c813_34 :: Nat -> c6:c7:c8 gen_c16:c17:c18:c19:c2014_34 :: Nat -> c16:c17:c18:c19:c20 Lemmas: mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3025630_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3025630_34), rt in Omega(0) a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3044649_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3044649_34)), rt in Omega(0) a__half(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3049071_34))) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3049071_34), rt in Omega(0) a__sqr(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3050242_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(n3050242_34, n3050242_34)), rt in Omega(0) a__add(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3021342_34), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(n3021342_34, b)), rt in Omega(0) Generator Equations: gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0) <=> 0' gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(x, 1)) <=> s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(x)) gen_c2:c3:c4:c510_34(0) <=> c2 gen_c2:c3:c4:c510_34(+(x, 1)) <=> c3(c9(c32), gen_c2:c3:c4:c510_34(x), c32) gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(0) <=> c32 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(+(x, 1)) <=> c21(c(c2, c32), gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(x)) gen_c9:c10:c11:c1212_34(0) <=> c9(c32) gen_c9:c10:c11:c1212_34(+(x, 1)) <=> c10(gen_c9:c10:c11:c1212_34(x), c32) gen_c6:c7:c813_34(0) <=> c6 gen_c6:c7:c813_34(+(x, 1)) <=> c7(gen_c6:c7:c813_34(x), c32) gen_c16:c17:c18:c19:c2014_34(0) <=> c16 gen_c16:c17:c18:c19:c2014_34(+(x, 1)) <=> c18(gen_c16:c17:c18:c19:c2014_34(x), c32) The following defined symbols remain to be analysed: A__SQR, A__TERMS, MARK, A__ADD, A__DBL, A__HALF They will be analysed ascendingly in the following order: A__TERMS = A__SQR A__TERMS = MARK A__TERMS = A__ADD A__TERMS = A__DBL A__TERMS = A__HALF A__SQR = MARK A__SQR = A__ADD A__SQR = A__DBL A__SQR = A__HALF MARK = A__ADD MARK = A__DBL MARK = A__HALF A__ADD = A__DBL A__ADD = A__HALF A__DBL = A__HALF ---------------------------------------- (33) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: A__ADD(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3096607_34), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)) -> *15_34, rt in Omega(n3096607_34) Induction Base: A__ADD(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)) Induction Step: A__ADD(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(n3096607_34, 1)), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)) ->_R^Omega(1) c10(A__ADD(mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3096607_34)), mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b))), MARK(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3096607_34))) ->_L^Omega(0) c10(A__ADD(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3096607_34), mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b))), MARK(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3096607_34))) ->_L^Omega(0) c10(A__ADD(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3096607_34), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)), MARK(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3096607_34))) ->_IH c10(*15_34, MARK(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3096607_34))) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (34) Complex Obligation (BEST) ---------------------------------------- (35) Obligation: Proved the lower bound n^1 for the following 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__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__SQR(z0) -> c5 A__DBL(0') -> c6 A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__DBL(z0) -> c8 A__ADD(0', z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c12 A__FIRST(0', z0) -> c13 A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__FIRST(z0, z1) -> c15 A__HALF(0') -> c16 A__HALF(s(0')) -> c17 A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) A__HALF(z0) -> c20 MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) MARK(0') -> c32 MARK(nil) -> c33 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0') -> 0' a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0', z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0') -> 0' a__half(s(0')) -> 0' a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' mark(nil) -> nil Types: A__TERMS :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c:c1 c :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c:c1 A__SQR :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c2:c3:c4:c5 mark :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil MARK :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c1 :: c:c1 0' :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c2 :: c2:c3:c4:c5 s :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c3 :: c9:c10:c11:c12 -> c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__ADD :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c9:c10:c11:c12 a__sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c4 :: c9:c10:c11:c12 -> c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__DBL :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c6:c7:c8 c5 :: c2:c3:c4:c5 c6 :: c6:c7:c8 c7 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c6:c7:c8 c8 :: c6:c7:c8 c9 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c10 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c11 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c12 :: c9:c10:c11:c12 A__FIRST :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c13:c14:c15 c13 :: c13:c14:c15 cons :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c14 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c13:c14:c15 c15 :: c13:c14:c15 A__HALF :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c16:c17:c18:c19:c20 c16 :: c16:c17:c18:c19:c20 c17 :: c16:c17:c18:c19:c20 c18 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c19 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 c20 :: c16:c17:c18:c19:c20 terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c21 :: c:c1 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c22 :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c23 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c24 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c25 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c26 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c27 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c28 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c29 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 recip :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c30 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c31 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c32 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 nil :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c33 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 a__terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c:c11_34 :: c:c1 hole_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil2_34 :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c2:c3:c4:c53_34 :: c2:c3:c4:c5 hole_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c334_34 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 hole_c9:c10:c11:c125_34 :: c9:c10:c11:c12 hole_c6:c7:c86_34 :: c6:c7:c8 hole_c13:c14:c157_34 :: c13:c14:c15 hole_c16:c17:c18:c19:c208_34 :: c16:c17:c18:c19:c20 gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34 :: Nat -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil gen_c2:c3:c4:c510_34 :: Nat -> c2:c3:c4:c5 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34 :: Nat -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 gen_c9:c10:c11:c1212_34 :: Nat -> c9:c10:c11:c12 gen_c6:c7:c813_34 :: Nat -> c6:c7:c8 gen_c16:c17:c18:c19:c2014_34 :: Nat -> c16:c17:c18:c19:c20 Lemmas: mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3025630_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3025630_34), rt in Omega(0) a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3044649_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3044649_34)), rt in Omega(0) a__half(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3049071_34))) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3049071_34), rt in Omega(0) a__sqr(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3050242_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(n3050242_34, n3050242_34)), rt in Omega(0) a__add(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3021342_34), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(n3021342_34, b)), rt in Omega(0) Generator Equations: gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0) <=> 0' gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(x, 1)) <=> s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(x)) gen_c2:c3:c4:c510_34(0) <=> c2 gen_c2:c3:c4:c510_34(+(x, 1)) <=> c3(c9(c32), gen_c2:c3:c4:c510_34(x), c32) gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(0) <=> c32 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(+(x, 1)) <=> c21(c(c2, c32), gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(x)) gen_c9:c10:c11:c1212_34(0) <=> c9(c32) gen_c9:c10:c11:c1212_34(+(x, 1)) <=> c10(gen_c9:c10:c11:c1212_34(x), c32) gen_c6:c7:c813_34(0) <=> c6 gen_c6:c7:c813_34(+(x, 1)) <=> c7(gen_c6:c7:c813_34(x), c32) gen_c16:c17:c18:c19:c2014_34(0) <=> c16 gen_c16:c17:c18:c19:c2014_34(+(x, 1)) <=> c18(gen_c16:c17:c18:c19:c2014_34(x), c32) The following defined symbols remain to be analysed: A__ADD, A__TERMS, MARK, A__DBL, A__HALF They will be analysed ascendingly in the following order: A__TERMS = A__SQR A__TERMS = MARK A__TERMS = A__ADD A__TERMS = A__DBL A__TERMS = A__HALF A__SQR = MARK A__SQR = A__ADD A__SQR = A__DBL A__SQR = A__HALF MARK = A__ADD MARK = A__DBL MARK = A__HALF A__ADD = A__DBL A__ADD = A__HALF A__DBL = A__HALF ---------------------------------------- (36) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (37) BOUNDS(n^1, INF) ---------------------------------------- (38) 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__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__SQR(z0) -> c5 A__DBL(0') -> c6 A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__DBL(z0) -> c8 A__ADD(0', z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c12 A__FIRST(0', z0) -> c13 A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__FIRST(z0, z1) -> c15 A__HALF(0') -> c16 A__HALF(s(0')) -> c17 A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) A__HALF(z0) -> c20 MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) MARK(0') -> c32 MARK(nil) -> c33 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0') -> 0' a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0', z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0') -> 0' a__half(s(0')) -> 0' a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' mark(nil) -> nil Types: A__TERMS :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c:c1 c :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c:c1 A__SQR :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c2:c3:c4:c5 mark :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil MARK :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c1 :: c:c1 0' :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c2 :: c2:c3:c4:c5 s :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c3 :: c9:c10:c11:c12 -> c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__ADD :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c9:c10:c11:c12 a__sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c4 :: c9:c10:c11:c12 -> c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__DBL :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c6:c7:c8 c5 :: c2:c3:c4:c5 c6 :: c6:c7:c8 c7 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c6:c7:c8 c8 :: c6:c7:c8 c9 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c10 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c11 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c12 :: c9:c10:c11:c12 A__FIRST :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c13:c14:c15 c13 :: c13:c14:c15 cons :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c14 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c13:c14:c15 c15 :: c13:c14:c15 A__HALF :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c16:c17:c18:c19:c20 c16 :: c16:c17:c18:c19:c20 c17 :: c16:c17:c18:c19:c20 c18 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c19 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 c20 :: c16:c17:c18:c19:c20 terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c21 :: c:c1 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c22 :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c23 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c24 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c25 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c26 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c27 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c28 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c29 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 recip :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c30 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c31 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c32 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 nil :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c33 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 a__terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c:c11_34 :: c:c1 hole_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil2_34 :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c2:c3:c4:c53_34 :: c2:c3:c4:c5 hole_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c334_34 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 hole_c9:c10:c11:c125_34 :: c9:c10:c11:c12 hole_c6:c7:c86_34 :: c6:c7:c8 hole_c13:c14:c157_34 :: c13:c14:c15 hole_c16:c17:c18:c19:c208_34 :: c16:c17:c18:c19:c20 gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34 :: Nat -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil gen_c2:c3:c4:c510_34 :: Nat -> c2:c3:c4:c5 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34 :: Nat -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 gen_c9:c10:c11:c1212_34 :: Nat -> c9:c10:c11:c12 gen_c6:c7:c813_34 :: Nat -> c6:c7:c8 gen_c16:c17:c18:c19:c2014_34 :: Nat -> c16:c17:c18:c19:c20 Lemmas: mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3025630_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3025630_34), rt in Omega(0) a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3044649_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3044649_34)), rt in Omega(0) a__half(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3049071_34))) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3049071_34), rt in Omega(0) a__sqr(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3050242_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(n3050242_34, n3050242_34)), rt in Omega(0) a__add(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3021342_34), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(n3021342_34, b)), rt in Omega(0) A__ADD(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3096607_34), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)) -> *15_34, rt in Omega(n3096607_34) Generator Equations: gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0) <=> 0' gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(x, 1)) <=> s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(x)) gen_c2:c3:c4:c510_34(0) <=> c2 gen_c2:c3:c4:c510_34(+(x, 1)) <=> c3(c9(c32), gen_c2:c3:c4:c510_34(x), c32) gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(0) <=> c32 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(+(x, 1)) <=> c21(c(c2, c32), gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(x)) gen_c9:c10:c11:c1212_34(0) <=> c9(c32) gen_c9:c10:c11:c1212_34(+(x, 1)) <=> c10(gen_c9:c10:c11:c1212_34(x), c32) gen_c6:c7:c813_34(0) <=> c6 gen_c6:c7:c813_34(+(x, 1)) <=> c7(gen_c6:c7:c813_34(x), c32) gen_c16:c17:c18:c19:c2014_34(0) <=> c16 gen_c16:c17:c18:c19:c2014_34(+(x, 1)) <=> c18(gen_c16:c17:c18:c19:c2014_34(x), c32) The following defined symbols remain to be analysed: MARK, A__TERMS, A__SQR, A__DBL, A__HALF They will be analysed ascendingly in the following order: A__TERMS = A__SQR A__TERMS = MARK A__TERMS = A__ADD A__TERMS = A__DBL A__TERMS = A__HALF A__SQR = MARK A__SQR = A__ADD A__SQR = A__DBL A__SQR = A__HALF MARK = A__ADD MARK = A__DBL MARK = A__HALF A__ADD = A__DBL A__ADD = A__HALF A__DBL = A__HALF ---------------------------------------- (39) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: MARK(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(1, n4070917_34))) -> *15_34, rt in Omega(n4070917_34) Induction Base: MARK(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(1, 0))) Induction Step: MARK(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(1, +(n4070917_34, 1)))) ->_R^Omega(1) c31(MARK(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(1, n4070917_34)))) ->_IH c31(*15_34) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (40) Obligation: Innermost TRS: Rules: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__TERMS(z0) -> c1 A__SQR(0') -> c2 A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__SQR(z0) -> c5 A__DBL(0') -> c6 A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__DBL(z0) -> c8 A__ADD(0', z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c12 A__FIRST(0', z0) -> c13 A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__FIRST(z0, z1) -> c15 A__HALF(0') -> c16 A__HALF(s(0')) -> c17 A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) A__HALF(z0) -> c20 MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) MARK(0') -> c32 MARK(nil) -> c33 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0') -> 0' a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0', z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0') -> 0' a__half(s(0')) -> 0' a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' mark(nil) -> nil Types: A__TERMS :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c:c1 c :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c:c1 A__SQR :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c2:c3:c4:c5 mark :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil MARK :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c1 :: c:c1 0' :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c2 :: c2:c3:c4:c5 s :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c3 :: c9:c10:c11:c12 -> c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__ADD :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c9:c10:c11:c12 a__sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c4 :: c9:c10:c11:c12 -> c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__DBL :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c6:c7:c8 c5 :: c2:c3:c4:c5 c6 :: c6:c7:c8 c7 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c6:c7:c8 c8 :: c6:c7:c8 c9 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c10 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c11 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c12 :: c9:c10:c11:c12 A__FIRST :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c13:c14:c15 c13 :: c13:c14:c15 cons :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c14 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c13:c14:c15 c15 :: c13:c14:c15 A__HALF :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c16:c17:c18:c19:c20 c16 :: c16:c17:c18:c19:c20 c17 :: c16:c17:c18:c19:c20 c18 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c19 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 c20 :: c16:c17:c18:c19:c20 terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c21 :: c:c1 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c22 :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c23 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c24 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c25 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c26 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c27 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c28 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c29 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 recip :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c30 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c31 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c32 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 nil :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c33 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 a__terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c:c11_34 :: c:c1 hole_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil2_34 :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c2:c3:c4:c53_34 :: c2:c3:c4:c5 hole_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c334_34 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 hole_c9:c10:c11:c125_34 :: c9:c10:c11:c12 hole_c6:c7:c86_34 :: c6:c7:c8 hole_c13:c14:c157_34 :: c13:c14:c15 hole_c16:c17:c18:c19:c208_34 :: c16:c17:c18:c19:c20 gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34 :: Nat -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil gen_c2:c3:c4:c510_34 :: Nat -> c2:c3:c4:c5 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34 :: Nat -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 gen_c9:c10:c11:c1212_34 :: Nat -> c9:c10:c11:c12 gen_c6:c7:c813_34 :: Nat -> c6:c7:c8 gen_c16:c17:c18:c19:c2014_34 :: Nat -> c16:c17:c18:c19:c20 Lemmas: mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3025630_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3025630_34), rt in Omega(0) a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3044649_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3044649_34)), rt in Omega(0) a__half(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3049071_34))) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3049071_34), rt in Omega(0) a__sqr(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3050242_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(n3050242_34, n3050242_34)), rt in Omega(0) a__add(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3021342_34), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(n3021342_34, b)), rt in Omega(0) A__ADD(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3096607_34), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)) -> *15_34, rt in Omega(n3096607_34) MARK(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(1, n4070917_34))) -> *15_34, rt in Omega(n4070917_34) Generator Equations: gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0) <=> 0' gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(x, 1)) <=> s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(x)) gen_c2:c3:c4:c510_34(0) <=> c2 gen_c2:c3:c4:c510_34(+(x, 1)) <=> c3(c9(c32), gen_c2:c3:c4:c510_34(x), c32) gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(0) <=> c32 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(+(x, 1)) <=> c21(c(c2, c32), gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(x)) gen_c9:c10:c11:c1212_34(0) <=> c9(c32) gen_c9:c10:c11:c1212_34(+(x, 1)) <=> c10(gen_c9:c10:c11:c1212_34(x), c32) gen_c6:c7:c813_34(0) <=> c6 gen_c6:c7:c813_34(+(x, 1)) <=> c7(gen_c6:c7:c813_34(x), c32) gen_c16:c17:c18:c19:c2014_34(0) <=> c16 gen_c16:c17:c18:c19:c2014_34(+(x, 1)) <=> c18(gen_c16:c17:c18:c19:c2014_34(x), c32) The following defined symbols remain to be analysed: A__TERMS, A__SQR, A__ADD, A__DBL, A__HALF They will be analysed ascendingly in the following order: A__TERMS = A__SQR A__TERMS = MARK A__TERMS = A__ADD A__TERMS = A__DBL A__TERMS = A__HALF A__SQR = MARK A__SQR = A__ADD A__SQR = A__DBL A__SQR = A__HALF MARK = A__ADD MARK = A__DBL MARK = A__HALF A__ADD = A__DBL A__ADD = A__HALF A__DBL = A__HALF ---------------------------------------- (41) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: A__DBL(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n4396163_34)) -> *15_34, rt in Omega(n4396163_34) Induction Base: A__DBL(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0)) Induction Step: A__DBL(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(n4396163_34, 1))) ->_R^Omega(1) c7(A__DBL(mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n4396163_34))), MARK(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n4396163_34))) ->_L^Omega(0) c7(A__DBL(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n4396163_34)), MARK(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n4396163_34))) ->_IH c7(*15_34, MARK(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n4396163_34))) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (42) Obligation: Innermost TRS: Rules: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__TERMS(z0) -> c1 A__SQR(0') -> c2 A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__SQR(z0) -> c5 A__DBL(0') -> c6 A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__DBL(z0) -> c8 A__ADD(0', z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c12 A__FIRST(0', z0) -> c13 A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__FIRST(z0, z1) -> c15 A__HALF(0') -> c16 A__HALF(s(0')) -> c17 A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) A__HALF(z0) -> c20 MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) MARK(0') -> c32 MARK(nil) -> c33 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0') -> 0' a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0', z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0') -> 0' a__half(s(0')) -> 0' a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' mark(nil) -> nil Types: A__TERMS :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c:c1 c :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c:c1 A__SQR :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c2:c3:c4:c5 mark :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil MARK :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c1 :: c:c1 0' :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c2 :: c2:c3:c4:c5 s :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c3 :: c9:c10:c11:c12 -> c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__ADD :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c9:c10:c11:c12 a__sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c4 :: c9:c10:c11:c12 -> c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__DBL :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c6:c7:c8 c5 :: c2:c3:c4:c5 c6 :: c6:c7:c8 c7 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c6:c7:c8 c8 :: c6:c7:c8 c9 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c10 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c11 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c12 :: c9:c10:c11:c12 A__FIRST :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c13:c14:c15 c13 :: c13:c14:c15 cons :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c14 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c13:c14:c15 c15 :: c13:c14:c15 A__HALF :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c16:c17:c18:c19:c20 c16 :: c16:c17:c18:c19:c20 c17 :: c16:c17:c18:c19:c20 c18 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c19 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 c20 :: c16:c17:c18:c19:c20 terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c21 :: c:c1 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c22 :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c23 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c24 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c25 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c26 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c27 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c28 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c29 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 recip :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c30 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c31 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c32 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 nil :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c33 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 a__terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c:c11_34 :: c:c1 hole_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil2_34 :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c2:c3:c4:c53_34 :: c2:c3:c4:c5 hole_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c334_34 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 hole_c9:c10:c11:c125_34 :: c9:c10:c11:c12 hole_c6:c7:c86_34 :: c6:c7:c8 hole_c13:c14:c157_34 :: c13:c14:c15 hole_c16:c17:c18:c19:c208_34 :: c16:c17:c18:c19:c20 gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34 :: Nat -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil gen_c2:c3:c4:c510_34 :: Nat -> c2:c3:c4:c5 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34 :: Nat -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 gen_c9:c10:c11:c1212_34 :: Nat -> c9:c10:c11:c12 gen_c6:c7:c813_34 :: Nat -> c6:c7:c8 gen_c16:c17:c18:c19:c2014_34 :: Nat -> c16:c17:c18:c19:c20 Lemmas: mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3025630_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3025630_34), rt in Omega(0) a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3044649_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3044649_34)), rt in Omega(0) a__half(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3049071_34))) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3049071_34), rt in Omega(0) a__sqr(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3050242_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(n3050242_34, n3050242_34)), rt in Omega(0) a__add(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3021342_34), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(n3021342_34, b)), rt in Omega(0) A__ADD(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3096607_34), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)) -> *15_34, rt in Omega(n3096607_34) MARK(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(1, n4070917_34))) -> *15_34, rt in Omega(n4070917_34) A__DBL(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n4396163_34)) -> *15_34, rt in Omega(n4396163_34) Generator Equations: gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0) <=> 0' gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(x, 1)) <=> s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(x)) gen_c2:c3:c4:c510_34(0) <=> c2 gen_c2:c3:c4:c510_34(+(x, 1)) <=> c3(c9(c32), gen_c2:c3:c4:c510_34(x), c32) gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(0) <=> c32 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(+(x, 1)) <=> c21(c(c2, c32), gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(x)) gen_c9:c10:c11:c1212_34(0) <=> c9(c32) gen_c9:c10:c11:c1212_34(+(x, 1)) <=> c10(gen_c9:c10:c11:c1212_34(x), c32) gen_c6:c7:c813_34(0) <=> c6 gen_c6:c7:c813_34(+(x, 1)) <=> c7(gen_c6:c7:c813_34(x), c32) gen_c16:c17:c18:c19:c2014_34(0) <=> c16 gen_c16:c17:c18:c19:c2014_34(+(x, 1)) <=> c18(gen_c16:c17:c18:c19:c2014_34(x), c32) The following defined symbols remain to be analysed: A__HALF, A__TERMS, A__SQR, MARK, A__ADD They will be analysed ascendingly in the following order: A__TERMS = A__SQR A__TERMS = MARK A__TERMS = A__ADD A__TERMS = A__DBL A__TERMS = A__HALF A__SQR = MARK A__SQR = A__ADD A__SQR = A__DBL A__SQR = A__HALF MARK = A__ADD MARK = A__DBL MARK = A__HALF A__ADD = A__DBL A__ADD = A__HALF A__DBL = A__HALF ---------------------------------------- (43) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: A__HALF(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n6270734_34))) -> *15_34, rt in Omega(n6270734_34) Induction Base: A__HALF(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, 0))) Induction Step: A__HALF(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, +(n6270734_34, 1)))) ->_R^Omega(1) c18(A__HALF(mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n6270734_34)))), MARK(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n6270734_34)))) ->_L^Omega(0) c18(A__HALF(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n6270734_34))), MARK(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n6270734_34)))) ->_IH c18(*15_34, MARK(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n6270734_34)))) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (44) Obligation: Innermost TRS: Rules: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__TERMS(z0) -> c1 A__SQR(0') -> c2 A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__SQR(z0) -> c5 A__DBL(0') -> c6 A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__DBL(z0) -> c8 A__ADD(0', z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c12 A__FIRST(0', z0) -> c13 A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__FIRST(z0, z1) -> c15 A__HALF(0') -> c16 A__HALF(s(0')) -> c17 A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) A__HALF(z0) -> c20 MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) MARK(0') -> c32 MARK(nil) -> c33 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0') -> 0' a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0', z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0') -> 0' a__half(s(0')) -> 0' a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' mark(nil) -> nil Types: A__TERMS :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c:c1 c :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c:c1 A__SQR :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c2:c3:c4:c5 mark :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil MARK :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c1 :: c:c1 0' :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c2 :: c2:c3:c4:c5 s :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c3 :: c9:c10:c11:c12 -> c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__ADD :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c9:c10:c11:c12 a__sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c4 :: c9:c10:c11:c12 -> c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c2:c3:c4:c5 A__DBL :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c6:c7:c8 c5 :: c2:c3:c4:c5 c6 :: c6:c7:c8 c7 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c6:c7:c8 c8 :: c6:c7:c8 c9 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c10 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c11 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12 c12 :: c9:c10:c11:c12 A__FIRST :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c13:c14:c15 c13 :: c13:c14:c15 cons :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c14 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c13:c14:c15 c15 :: c13:c14:c15 A__HALF :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> c16:c17:c18:c19:c20 c16 :: c16:c17:c18:c19:c20 c17 :: c16:c17:c18:c19:c20 c18 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 dbl :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c19 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18:c19:c20 c20 :: c16:c17:c18:c19:c20 terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c21 :: c:c1 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 sqr :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c22 :: c2:c3:c4:c5 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c23 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c24 :: c9:c10:c11:c12 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c25 :: c6:c7:c8 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c26 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c27 :: c13:c14:c15 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c28 :: c16:c17:c18:c19:c20 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c29 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 recip :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c30 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c31 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c32 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 nil :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil c33 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 a__terms :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__add :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__first :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil a__half :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c:c11_34 :: c:c1 hole_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil2_34 :: 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil hole_c2:c3:c4:c53_34 :: c2:c3:c4:c5 hole_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c334_34 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 hole_c9:c10:c11:c125_34 :: c9:c10:c11:c12 hole_c6:c7:c86_34 :: c6:c7:c8 hole_c13:c14:c157_34 :: c13:c14:c15 hole_c16:c17:c18:c19:c208_34 :: c16:c17:c18:c19:c20 gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34 :: Nat -> 0':s:cons:dbl:terms:sqr:add:first:half:recip:nil gen_c2:c3:c4:c510_34 :: Nat -> c2:c3:c4:c5 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34 :: Nat -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 gen_c9:c10:c11:c1212_34 :: Nat -> c9:c10:c11:c12 gen_c6:c7:c813_34 :: Nat -> c6:c7:c8 gen_c16:c17:c18:c19:c2014_34 :: Nat -> c16:c17:c18:c19:c20 Lemmas: mark(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3025630_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3025630_34), rt in Omega(0) a__dbl(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3044649_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3044649_34)), rt in Omega(0) a__half(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n3049071_34))) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3049071_34), rt in Omega(0) a__sqr(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3050242_34)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(n3050242_34, n3050242_34)), rt in Omega(0) a__add(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3021342_34), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)) -> gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(n3021342_34, b)), rt in Omega(0) A__ADD(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n3096607_34), gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(b)) -> *15_34, rt in Omega(n3096607_34) MARK(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(1, n4070917_34))) -> *15_34, rt in Omega(n4070917_34) A__DBL(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(n4396163_34)) -> *15_34, rt in Omega(n4396163_34) A__HALF(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(*(2, n6270734_34))) -> *15_34, rt in Omega(n6270734_34) Generator Equations: gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(0) <=> 0' gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(+(x, 1)) <=> s(gen_0':s:cons:dbl:terms:sqr:add:first:half:recip:nil9_34(x)) gen_c2:c3:c4:c510_34(0) <=> c2 gen_c2:c3:c4:c510_34(+(x, 1)) <=> c3(c9(c32), gen_c2:c3:c4:c510_34(x), c32) gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(0) <=> c32 gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(+(x, 1)) <=> c21(c(c2, c32), gen_c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(x)) gen_c9:c10:c11:c1212_34(0) <=> c9(c32) gen_c9:c10:c11:c1212_34(+(x, 1)) <=> c10(gen_c9:c10:c11:c1212_34(x), c32) gen_c6:c7:c813_34(0) <=> c6 gen_c6:c7:c813_34(+(x, 1)) <=> c7(gen_c6:c7:c813_34(x), c32) gen_c16:c17:c18:c19:c2014_34(0) <=> c16 gen_c16:c17:c18:c19:c2014_34(+(x, 1)) <=> c18(gen_c16:c17:c18:c19:c2014_34(x), c32) The following defined symbols remain to be analysed: A__SQR, A__TERMS, MARK, A__ADD, A__DBL They will be analysed ascendingly in the following order: A__TERMS = A__SQR A__TERMS = MARK A__TERMS = A__ADD A__TERMS = A__DBL A__TERMS = A__HALF A__SQR = MARK A__SQR = A__ADD A__SQR = A__DBL A__SQR = A__HALF MARK = A__ADD MARK = A__DBL MARK = A__HALF A__ADD = A__DBL A__ADD = A__HALF A__DBL = A__HALF ---------------------------------------- (45) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (46) 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(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__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__SQR(z0) -> c5 A__DBL(0) -> c6 A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__DBL(z0) -> c8 A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c12 A__FIRST(0, z0) -> c13 A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__FIRST(z0, z1) -> c15 A__HALF(0) -> c16 A__HALF(s(0)) -> c17 A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) A__HALF(z0) -> c20 MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) MARK(0) -> c32 MARK(nil) -> c33 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__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__SQR(z0) -> c5 A__DBL(0) -> c6 A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__DBL(z0) -> c8 A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c12 A__FIRST(0, z0) -> c13 A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__FIRST(z0, z1) -> c15 A__HALF(0) -> c16 A__HALF(s(0)) -> c17 A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) A__HALF(z0) -> c20 MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) MARK(0) -> c32 MARK(nil) -> c33 K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__TERMS_1, A__SQR_1, A__DBL_1, A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1 Compound Symbols: c_2, c1, c2, c3_3, c4_3, c5, c6, c7_2, c8, c9_1, c10_2, c11_2, c12, c13, c14_1, c15, c16, c17, c18_2, c19_1, c20, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c32, c33 ---------------------------------------- (47) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 13 trailing nodes: MARK(nil) -> c33 A__DBL(0) -> c6 A__DBL(z0) -> c8 A__TERMS(z0) -> c1 MARK(0) -> c32 A__FIRST(z0, z1) -> c15 A__HALF(z0) -> c20 A__SQR(0) -> c2 A__HALF(s(0)) -> c17 A__FIRST(0, z0) -> c13 A__SQR(z0) -> c5 A__ADD(z0, z1) -> c12 A__HALF(0) -> c16 ---------------------------------------- (48) 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) S tuples: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__TERMS_1, A__SQR_1, A__DBL_1, A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1 Compound Symbols: c_2, c3_3, c4_3, c7_2, c9_1, c10_2, c11_2, c14_1, c18_2, c19_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1 ---------------------------------------- (49) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (50) 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__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Rewrite Strategy: INNERMOST ---------------------------------------- (51) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (52) 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__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (53) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (54) 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(z0) -> c(A__SQR(mark(z0)), MARK(z0)) [1] A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) [1] A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) [1] A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) [1] A__ADD(0, z0) -> c9(MARK(z0)) [1] A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) [1] A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) [1] A__HALF(dbl(z0)) -> c19(MARK(z0)) [1] MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) [1] MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) [1] MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) [1] MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) [1] MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) [1] MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) [1] MARK(cons(z0, z1)) -> c29(MARK(z0)) [1] MARK(recip(z0)) -> c30(MARK(z0)) [1] MARK(s(z0)) -> c31(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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) [0] a__sqr(z0) -> sqr(z0) [0] a__dbl(0) -> 0 [0] a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) [0] a__dbl(z0) -> dbl(z0) [0] a__add(0, z0) -> mark(z0) [0] a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) [0] a__add(z0, z1) -> add(z0, z1) [0] a__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] a__half(0) -> 0 [0] a__half(s(0)) -> 0 [0] a__half(s(s(z0))) -> s(a__half(mark(z0))) [0] a__half(dbl(z0)) -> mark(z0) [0] a__half(z0) -> half(z0) [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(half(z0)) -> a__half(mark(z0)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(recip(z0)) -> recip(mark(z0)) [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] mark(nil) -> nil [0] Rewrite Strategy: INNERMOST ---------------------------------------- (55) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (56) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) [1] A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) [1] A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) [1] A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) [1] A__ADD(0, z0) -> c9(MARK(z0)) [1] A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) [1] A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) [1] A__HALF(dbl(z0)) -> c19(MARK(z0)) [1] MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) [1] MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) [1] MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) [1] MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) [1] MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) [1] MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) [1] MARK(cons(z0, z1)) -> c29(MARK(z0)) [1] MARK(recip(z0)) -> c30(MARK(z0)) [1] MARK(s(z0)) -> c31(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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) [0] a__sqr(z0) -> sqr(z0) [0] a__dbl(0) -> 0 [0] a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) [0] a__dbl(z0) -> dbl(z0) [0] a__add(0, z0) -> mark(z0) [0] a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) [0] a__add(z0, z1) -> add(z0, z1) [0] a__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] a__half(0) -> 0 [0] a__half(s(0)) -> 0 [0] a__half(s(s(z0))) -> s(a__half(mark(z0))) [0] a__half(dbl(z0)) -> mark(z0) [0] a__half(z0) -> half(z0) [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(half(z0)) -> a__half(mark(z0)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(recip(z0)) -> recip(mark(z0)) [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] mark(nil) -> nil [0] The TRS has the following type information: A__TERMS :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> c c :: c3:c4 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c A__SQR :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> c3:c4 mark :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil MARK :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 s :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil c3 :: c9:c10:c11 -> c3:c4 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c3:c4 A__ADD :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> c9:c10:c11 a__sqr :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil a__dbl :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil c4 :: c9:c10:c11 -> c7 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c3:c4 A__DBL :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> c7 c7 :: c7 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c7 0 :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil c9 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c9:c10:c11 c10 :: c9:c10:c11 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c9:c10:c11 c11 :: c9:c10:c11 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c9:c10:c11 A__FIRST :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> c14 cons :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil c14 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c14 A__HALF :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> c18:c19 c18 :: c18:c19 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19 dbl :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil c19 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19 terms :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil c21 :: c -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 sqr :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil c22 :: c3:c4 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 add :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil c23 :: c9:c10:c11 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c24 :: c9:c10:c11 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c25 :: c7 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 first :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil c26 :: c14 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c27 :: c14 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 half :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil c28 :: c18:c19 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c29 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 recip :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil c30 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c31 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 a__terms :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil a__add :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil a__first :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil nil :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil a__half :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil Rewrite Strategy: INNERMOST ---------------------------------------- (57) 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__TERMS_1 A__SQR_1 A__DBL_1 A__ADD_2 A__FIRST_2 A__HALF_1 MARK_1 (c) The following functions are completely defined: a__terms_1 a__sqr_1 a__dbl_1 a__add_2 a__first_2 a__half_1 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] a__half(v0) -> null_a__half [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_a__half, null_mark, const, const1, const2, const3, const4, const5, const6 ---------------------------------------- (58) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) [1] A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) [1] A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) [1] A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) [1] A__ADD(0, z0) -> c9(MARK(z0)) [1] A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) [1] A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) [1] A__HALF(dbl(z0)) -> c19(MARK(z0)) [1] MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) [1] MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) [1] MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) [1] MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) [1] MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) [1] MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) [1] MARK(cons(z0, z1)) -> c29(MARK(z0)) [1] MARK(recip(z0)) -> c30(MARK(z0)) [1] MARK(s(z0)) -> c31(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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) [0] a__sqr(z0) -> sqr(z0) [0] a__dbl(0) -> 0 [0] a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) [0] a__dbl(z0) -> dbl(z0) [0] a__add(0, z0) -> mark(z0) [0] a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) [0] a__add(z0, z1) -> add(z0, z1) [0] a__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] a__half(0) -> 0 [0] a__half(s(0)) -> 0 [0] a__half(s(s(z0))) -> s(a__half(mark(z0))) [0] a__half(dbl(z0)) -> mark(z0) [0] a__half(z0) -> half(z0) [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(half(z0)) -> a__half(mark(z0)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(recip(z0)) -> recip(mark(z0)) [0] mark(s(z0)) -> s(mark(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] a__half(v0) -> null_a__half [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__TERMS :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> c c :: c3:c4 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c A__SQR :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> c3:c4 mark :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark MARK :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 s :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c3 :: c9:c10:c11 -> c3:c4 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c3:c4 A__ADD :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> c9:c10:c11 a__sqr :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark a__dbl :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c4 :: c9:c10:c11 -> c7 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c3:c4 A__DBL :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> c7 c7 :: c7 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c7 0 :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c9 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c9:c10:c11 c10 :: c9:c10:c11 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c9:c10:c11 c11 :: c9:c10:c11 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c9:c10:c11 A__FIRST :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> c14 cons :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c14 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c14 A__HALF :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> c18:c19 c18 :: c18:c19 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19 dbl :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c19 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19 terms :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c21 :: c -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 sqr :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c22 :: c3:c4 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 add :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c23 :: c9:c10:c11 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c24 :: c9:c10:c11 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c25 :: c7 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 first :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c26 :: c14 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c27 :: c14 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 half :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c28 :: c18:c19 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c29 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 recip :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c30 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c31 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 a__terms :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark a__add :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark a__first :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark nil :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark a__half :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark null_a__terms :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark null_a__sqr :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark null_a__dbl :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark null_a__add :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark null_a__first :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark null_a__half :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark null_mark :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark const :: c const1 :: c3:c4 const2 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 const3 :: c9:c10:c11 const4 :: c7 const5 :: c14 const6 :: c18:c19 Rewrite Strategy: INNERMOST ---------------------------------------- (59) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (60) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__TERMS(terms(z0')) -> c(A__SQR(a__terms(mark(z0'))), MARK(terms(z0'))) [1] A__TERMS(sqr(z0'')) -> c(A__SQR(a__sqr(mark(z0''))), MARK(sqr(z0''))) [1] A__TERMS(add(z01, z1')) -> c(A__SQR(a__add(mark(z01), mark(z1'))), MARK(add(z01, z1'))) [1] A__TERMS(dbl(z02)) -> c(A__SQR(a__dbl(mark(z02))), MARK(dbl(z02))) [1] A__TERMS(first(z03, z1'')) -> c(A__SQR(a__first(mark(z03), mark(z1''))), MARK(first(z03, z1''))) [1] A__TERMS(half(z04)) -> c(A__SQR(a__half(mark(z04))), MARK(half(z04))) [1] A__TERMS(cons(z05, z11)) -> c(A__SQR(cons(mark(z05), z11)), MARK(cons(z05, z11))) [1] A__TERMS(recip(z06)) -> c(A__SQR(recip(mark(z06))), MARK(recip(z06))) [1] A__TERMS(s(z07)) -> c(A__SQR(s(mark(z07))), MARK(s(z07))) [1] A__TERMS(0) -> c(A__SQR(0), MARK(0)) [1] A__TERMS(nil) -> c(A__SQR(nil), MARK(nil)) [1] A__TERMS(z0) -> c(A__SQR(null_mark), MARK(z0)) [1] A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) [1] A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) [1] A__DBL(s(terms(z062))) -> c7(A__DBL(a__terms(mark(z062))), MARK(terms(z062))) [1] A__DBL(s(sqr(z063))) -> c7(A__DBL(a__sqr(mark(z063))), MARK(sqr(z063))) [1] A__DBL(s(add(z064, z120))) -> c7(A__DBL(a__add(mark(z064), mark(z120))), MARK(add(z064, z120))) [1] A__DBL(s(dbl(z065))) -> c7(A__DBL(a__dbl(mark(z065))), MARK(dbl(z065))) [1] A__DBL(s(first(z066, z121))) -> c7(A__DBL(a__first(mark(z066), mark(z121))), MARK(first(z066, z121))) [1] A__DBL(s(half(z067))) -> c7(A__DBL(a__half(mark(z067))), MARK(half(z067))) [1] A__DBL(s(cons(z068, z122))) -> c7(A__DBL(cons(mark(z068), z122)), MARK(cons(z068, z122))) [1] A__DBL(s(recip(z069))) -> c7(A__DBL(recip(mark(z069))), MARK(recip(z069))) [1] A__DBL(s(s(z070))) -> c7(A__DBL(s(mark(z070))), MARK(s(z070))) [1] A__DBL(s(0)) -> c7(A__DBL(0), MARK(0)) [1] A__DBL(s(nil)) -> c7(A__DBL(nil), MARK(nil)) [1] A__DBL(s(z0)) -> c7(A__DBL(null_mark), MARK(z0)) [1] A__ADD(0, z0) -> c9(MARK(z0)) [1] A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) [1] A__HALF(s(s(terms(z0305)))) -> c18(A__HALF(a__terms(mark(z0305))), MARK(terms(z0305))) [1] A__HALF(s(s(sqr(z0306)))) -> c18(A__HALF(a__sqr(mark(z0306))), MARK(sqr(z0306))) [1] A__HALF(s(s(add(z0307, z1101)))) -> c18(A__HALF(a__add(mark(z0307), mark(z1101))), MARK(add(z0307, z1101))) [1] A__HALF(s(s(dbl(z0308)))) -> c18(A__HALF(a__dbl(mark(z0308))), MARK(dbl(z0308))) [1] A__HALF(s(s(first(z0309, z1102)))) -> c18(A__HALF(a__first(mark(z0309), mark(z1102))), MARK(first(z0309, z1102))) [1] A__HALF(s(s(half(z0310)))) -> c18(A__HALF(a__half(mark(z0310))), MARK(half(z0310))) [1] A__HALF(s(s(cons(z0311, z1103)))) -> c18(A__HALF(cons(mark(z0311), z1103)), MARK(cons(z0311, z1103))) [1] A__HALF(s(s(recip(z0312)))) -> c18(A__HALF(recip(mark(z0312))), MARK(recip(z0312))) [1] A__HALF(s(s(s(z0313)))) -> c18(A__HALF(s(mark(z0313))), MARK(s(z0313))) [1] A__HALF(s(s(0))) -> c18(A__HALF(0), MARK(0)) [1] A__HALF(s(s(nil))) -> c18(A__HALF(nil), MARK(nil)) [1] A__HALF(s(s(z0))) -> c18(A__HALF(null_mark), MARK(z0)) [1] A__HALF(dbl(z0)) -> c19(MARK(z0)) [1] MARK(terms(terms(z0314))) -> c21(A__TERMS(a__terms(mark(z0314))), MARK(terms(z0314))) [1] MARK(terms(sqr(z0315))) -> c21(A__TERMS(a__sqr(mark(z0315))), MARK(sqr(z0315))) [1] MARK(terms(add(z0316, z1104))) -> c21(A__TERMS(a__add(mark(z0316), mark(z1104))), MARK(add(z0316, z1104))) [1] MARK(terms(dbl(z0317))) -> c21(A__TERMS(a__dbl(mark(z0317))), MARK(dbl(z0317))) [1] MARK(terms(first(z0318, z1105))) -> c21(A__TERMS(a__first(mark(z0318), mark(z1105))), MARK(first(z0318, z1105))) [1] MARK(terms(half(z0319))) -> c21(A__TERMS(a__half(mark(z0319))), MARK(half(z0319))) [1] MARK(terms(cons(z0320, z1106))) -> c21(A__TERMS(cons(mark(z0320), z1106)), MARK(cons(z0320, z1106))) [1] MARK(terms(recip(z0321))) -> c21(A__TERMS(recip(mark(z0321))), MARK(recip(z0321))) [1] MARK(terms(s(z0322))) -> c21(A__TERMS(s(mark(z0322))), MARK(s(z0322))) [1] MARK(terms(0)) -> c21(A__TERMS(0), MARK(0)) [1] MARK(terms(nil)) -> c21(A__TERMS(nil), MARK(nil)) [1] MARK(terms(z0)) -> c21(A__TERMS(null_mark), MARK(z0)) [1] MARK(sqr(terms(z0323))) -> c22(A__SQR(a__terms(mark(z0323))), MARK(terms(z0323))) [1] MARK(sqr(sqr(z0324))) -> c22(A__SQR(a__sqr(mark(z0324))), MARK(sqr(z0324))) [1] MARK(sqr(add(z0325, z1107))) -> c22(A__SQR(a__add(mark(z0325), mark(z1107))), MARK(add(z0325, z1107))) [1] MARK(sqr(dbl(z0326))) -> c22(A__SQR(a__dbl(mark(z0326))), MARK(dbl(z0326))) [1] MARK(sqr(first(z0327, z1108))) -> c22(A__SQR(a__first(mark(z0327), mark(z1108))), MARK(first(z0327, z1108))) [1] MARK(sqr(half(z0328))) -> c22(A__SQR(a__half(mark(z0328))), MARK(half(z0328))) [1] MARK(sqr(cons(z0329, z1109))) -> c22(A__SQR(cons(mark(z0329), z1109)), MARK(cons(z0329, z1109))) [1] MARK(sqr(recip(z0330))) -> c22(A__SQR(recip(mark(z0330))), MARK(recip(z0330))) [1] MARK(sqr(s(z0331))) -> c22(A__SQR(s(mark(z0331))), MARK(s(z0331))) [1] MARK(sqr(0)) -> c22(A__SQR(0), MARK(0)) [1] MARK(sqr(nil)) -> c22(A__SQR(nil), MARK(nil)) [1] MARK(sqr(z0)) -> c22(A__SQR(null_mark), MARK(z0)) [1] MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] MARK(dbl(terms(z0566))) -> c25(A__DBL(a__terms(mark(z0566))), MARK(terms(z0566))) [1] MARK(dbl(sqr(z0567))) -> c25(A__DBL(a__sqr(mark(z0567))), MARK(sqr(z0567))) [1] MARK(dbl(add(z0568, z1188))) -> c25(A__DBL(a__add(mark(z0568), mark(z1188))), MARK(add(z0568, z1188))) [1] MARK(dbl(dbl(z0569))) -> c25(A__DBL(a__dbl(mark(z0569))), MARK(dbl(z0569))) [1] MARK(dbl(first(z0570, z1189))) -> c25(A__DBL(a__first(mark(z0570), mark(z1189))), MARK(first(z0570, z1189))) [1] MARK(dbl(half(z0571))) -> c25(A__DBL(a__half(mark(z0571))), MARK(half(z0571))) [1] MARK(dbl(cons(z0572, z1190))) -> c25(A__DBL(cons(mark(z0572), z1190)), MARK(cons(z0572, z1190))) [1] MARK(dbl(recip(z0573))) -> c25(A__DBL(recip(mark(z0573))), MARK(recip(z0573))) [1] MARK(dbl(s(z0574))) -> c25(A__DBL(s(mark(z0574))), MARK(s(z0574))) [1] MARK(dbl(0)) -> c25(A__DBL(0), MARK(0)) [1] MARK(dbl(nil)) -> c25(A__DBL(nil), MARK(nil)) [1] MARK(dbl(z0)) -> c25(A__DBL(null_mark), MARK(z0)) [1] MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) [1] MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) [1] MARK(half(terms(z0809))) -> c28(A__HALF(a__terms(mark(z0809))), MARK(terms(z0809))) [1] MARK(half(sqr(z0810))) -> c28(A__HALF(a__sqr(mark(z0810))), MARK(sqr(z0810))) [1] MARK(half(add(z0811, z1269))) -> c28(A__HALF(a__add(mark(z0811), mark(z1269))), MARK(add(z0811, z1269))) [1] MARK(half(dbl(z0812))) -> c28(A__HALF(a__dbl(mark(z0812))), MARK(dbl(z0812))) [1] MARK(half(first(z0813, z1270))) -> c28(A__HALF(a__first(mark(z0813), mark(z1270))), MARK(first(z0813, z1270))) [1] MARK(half(half(z0814))) -> c28(A__HALF(a__half(mark(z0814))), MARK(half(z0814))) [1] MARK(half(cons(z0815, z1271))) -> c28(A__HALF(cons(mark(z0815), z1271)), MARK(cons(z0815, z1271))) [1] MARK(half(recip(z0816))) -> c28(A__HALF(recip(mark(z0816))), MARK(recip(z0816))) [1] MARK(half(s(z0817))) -> c28(A__HALF(s(mark(z0817))), MARK(s(z0817))) [1] MARK(half(0)) -> c28(A__HALF(0), MARK(0)) [1] MARK(half(nil)) -> c28(A__HALF(nil), MARK(nil)) [1] MARK(half(z0)) -> c28(A__HALF(null_mark), MARK(z0)) [1] MARK(cons(z0, z1)) -> c29(MARK(z0)) [1] MARK(recip(z0)) -> c30(MARK(z0)) [1] MARK(s(z0)) -> c31(MARK(z0)) [1] a__terms(terms(z0818)) -> cons(recip(a__sqr(a__terms(mark(z0818)))), terms(s(terms(z0818)))) [0] a__terms(sqr(z0819)) -> cons(recip(a__sqr(a__sqr(mark(z0819)))), terms(s(sqr(z0819)))) [0] a__terms(add(z0820, z1272)) -> cons(recip(a__sqr(a__add(mark(z0820), mark(z1272)))), terms(s(add(z0820, z1272)))) [0] a__terms(dbl(z0821)) -> cons(recip(a__sqr(a__dbl(mark(z0821)))), terms(s(dbl(z0821)))) [0] a__terms(first(z0822, z1273)) -> cons(recip(a__sqr(a__first(mark(z0822), mark(z1273)))), terms(s(first(z0822, z1273)))) [0] a__terms(half(z0823)) -> cons(recip(a__sqr(a__half(mark(z0823)))), terms(s(half(z0823)))) [0] a__terms(cons(z0824, z1274)) -> cons(recip(a__sqr(cons(mark(z0824), z1274))), terms(s(cons(z0824, z1274)))) [0] a__terms(recip(z0825)) -> cons(recip(a__sqr(recip(mark(z0825)))), terms(s(recip(z0825)))) [0] a__terms(s(z0826)) -> cons(recip(a__sqr(s(mark(z0826)))), terms(s(s(z0826)))) [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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) [0] a__sqr(z0) -> sqr(z0) [0] a__dbl(0) -> 0 [0] a__dbl(s(terms(z0845))) -> s(s(a__dbl(a__terms(mark(z0845))))) [0] a__dbl(s(sqr(z0846))) -> s(s(a__dbl(a__sqr(mark(z0846))))) [0] a__dbl(s(add(z0847, z1281))) -> s(s(a__dbl(a__add(mark(z0847), mark(z1281))))) [0] a__dbl(s(dbl(z0848))) -> s(s(a__dbl(a__dbl(mark(z0848))))) [0] a__dbl(s(first(z0849, z1282))) -> s(s(a__dbl(a__first(mark(z0849), mark(z1282))))) [0] a__dbl(s(half(z0850))) -> s(s(a__dbl(a__half(mark(z0850))))) [0] a__dbl(s(cons(z0851, z1283))) -> s(s(a__dbl(cons(mark(z0851), z1283)))) [0] a__dbl(s(recip(z0852))) -> s(s(a__dbl(recip(mark(z0852))))) [0] a__dbl(s(s(z0853))) -> s(s(a__dbl(s(mark(z0853))))) [0] a__dbl(s(0)) -> s(s(a__dbl(0))) [0] a__dbl(s(nil)) -> s(s(a__dbl(nil))) [0] a__dbl(s(z0)) -> s(s(a__dbl(null_mark))) [0] a__dbl(z0) -> dbl(z0) [0] a__add(0, z0) -> mark(z0) [0] a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) [0] a__add(z0, z1) -> add(z0, z1) [0] a__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] a__half(0) -> 0 [0] a__half(s(0)) -> 0 [0] a__half(s(s(terms(z0971)))) -> s(a__half(a__terms(mark(z0971)))) [0] a__half(s(s(sqr(z0972)))) -> s(a__half(a__sqr(mark(z0972)))) [0] a__half(s(s(add(z0973, z1323)))) -> s(a__half(a__add(mark(z0973), mark(z1323)))) [0] a__half(s(s(dbl(z0974)))) -> s(a__half(a__dbl(mark(z0974)))) [0] a__half(s(s(first(z0975, z1324)))) -> s(a__half(a__first(mark(z0975), mark(z1324)))) [0] a__half(s(s(half(z0976)))) -> s(a__half(a__half(mark(z0976)))) [0] a__half(s(s(cons(z0977, z1325)))) -> s(a__half(cons(mark(z0977), z1325))) [0] a__half(s(s(recip(z0978)))) -> s(a__half(recip(mark(z0978)))) [0] a__half(s(s(s(z0979)))) -> s(a__half(s(mark(z0979)))) [0] a__half(s(s(0))) -> s(a__half(0)) [0] a__half(s(s(nil))) -> s(a__half(nil)) [0] a__half(s(s(z0))) -> s(a__half(null_mark)) [0] a__half(dbl(z0)) -> mark(z0) [0] a__half(z0) -> half(z0) [0] mark(terms(terms(z0980))) -> a__terms(a__terms(mark(z0980))) [0] mark(terms(sqr(z0981))) -> a__terms(a__sqr(mark(z0981))) [0] mark(terms(add(z0982, z1326))) -> a__terms(a__add(mark(z0982), mark(z1326))) [0] mark(terms(dbl(z0983))) -> a__terms(a__dbl(mark(z0983))) [0] mark(terms(first(z0984, z1327))) -> a__terms(a__first(mark(z0984), mark(z1327))) [0] mark(terms(half(z0985))) -> a__terms(a__half(mark(z0985))) [0] mark(terms(cons(z0986, z1328))) -> a__terms(cons(mark(z0986), z1328)) [0] mark(terms(recip(z0987))) -> a__terms(recip(mark(z0987))) [0] mark(terms(s(z0988))) -> a__terms(s(mark(z0988))) [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(z0989))) -> a__sqr(a__terms(mark(z0989))) [0] mark(sqr(sqr(z0990))) -> a__sqr(a__sqr(mark(z0990))) [0] mark(sqr(add(z0991, z1329))) -> a__sqr(a__add(mark(z0991), mark(z1329))) [0] mark(sqr(dbl(z0992))) -> a__sqr(a__dbl(mark(z0992))) [0] mark(sqr(first(z0993, z1330))) -> a__sqr(a__first(mark(z0993), mark(z1330))) [0] mark(sqr(half(z0994))) -> a__sqr(a__half(mark(z0994))) [0] mark(sqr(cons(z0995, z1331))) -> a__sqr(cons(mark(z0995), z1331)) [0] mark(sqr(recip(z0996))) -> a__sqr(recip(mark(z0996))) [0] mark(sqr(s(z0997))) -> a__sqr(s(mark(z0997))) [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(z01115))) -> a__dbl(a__terms(mark(z01115))) [0] mark(dbl(sqr(z01116))) -> a__dbl(a__sqr(mark(z01116))) [0] mark(dbl(add(z01117, z1371))) -> a__dbl(a__add(mark(z01117), mark(z1371))) [0] mark(dbl(dbl(z01118))) -> a__dbl(a__dbl(mark(z01118))) [0] mark(dbl(first(z01119, z1372))) -> a__dbl(a__first(mark(z01119), mark(z1372))) [0] mark(dbl(half(z01120))) -> a__dbl(a__half(mark(z01120))) [0] mark(dbl(cons(z01121, z1373))) -> a__dbl(cons(mark(z01121), z1373)) [0] mark(dbl(recip(z01122))) -> a__dbl(recip(mark(z01122))) [0] mark(dbl(s(z01123))) -> a__dbl(s(mark(z01123))) [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(half(terms(z01241))) -> a__half(a__terms(mark(z01241))) [0] mark(half(sqr(z01242))) -> a__half(a__sqr(mark(z01242))) [0] mark(half(add(z01243, z1413))) -> a__half(a__add(mark(z01243), mark(z1413))) [0] mark(half(dbl(z01244))) -> a__half(a__dbl(mark(z01244))) [0] mark(half(first(z01245, z1414))) -> a__half(a__first(mark(z01245), mark(z1414))) [0] mark(half(half(z01246))) -> a__half(a__half(mark(z01246))) [0] mark(half(cons(z01247, z1415))) -> a__half(cons(mark(z01247), z1415)) [0] mark(half(recip(z01248))) -> a__half(recip(mark(z01248))) [0] mark(half(s(z01249))) -> a__half(s(mark(z01249))) [0] mark(half(0)) -> a__half(0) [0] mark(half(nil)) -> a__half(nil) [0] mark(half(z0)) -> a__half(null_mark) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(recip(z0)) -> recip(mark(z0)) [0] mark(s(z0)) -> s(mark(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] a__half(v0) -> null_a__half [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__TERMS :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> c c :: c3:c4 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c A__SQR :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> c3:c4 mark :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark MARK :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 s :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c3 :: c9:c10:c11 -> c3:c4 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c3:c4 A__ADD :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> c9:c10:c11 a__sqr :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark a__dbl :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c4 :: c9:c10:c11 -> c7 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c3:c4 A__DBL :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> c7 c7 :: c7 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c7 0 :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c9 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c9:c10:c11 c10 :: c9:c10:c11 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c9:c10:c11 c11 :: c9:c10:c11 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c9:c10:c11 A__FIRST :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> c14 cons :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c14 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c14 A__HALF :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> c18:c19 c18 :: c18:c19 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19 dbl :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c19 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19 terms :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c21 :: c -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 sqr :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c22 :: c3:c4 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 add :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c23 :: c9:c10:c11 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c24 :: c9:c10:c11 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c25 :: c7 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 first :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c26 :: c14 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c27 :: c14 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 half :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c28 :: c18:c19 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c29 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 recip :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c30 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c31 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 a__terms :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark a__add :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark a__first :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark nil :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark a__half :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark null_a__terms :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark null_a__sqr :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark null_a__dbl :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark null_a__add :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark null_a__first :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark null_a__half :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark null_mark :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark const :: c const1 :: c3:c4 const2 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 const3 :: c9:c10:c11 const4 :: c7 const5 :: c14 const6 :: c18:c19 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_a__half => 0 null_mark => 0 const => 0 const1 => 0 const2 => 0 const3 => 0 const4 => 0 const5 => 0 const6 => 0 ---------------------------------------- (62) Obligation: Complexity RNTS consisting of the following rules: A__ADD(z, z') -{ 1 }-> 1 + MARK(z0) :|: z0 >= 0, z = 0, z' = z0 A__ADD(z, z') -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 A__ADD(z, z') -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 A__DBL(z) -{ 1 }-> 1 + A__DBL(a__terms(mark(z062))) + MARK(1 + z062) :|: z062 >= 0, z = 1 + (1 + z062) A__DBL(z) -{ 1 }-> 1 + A__DBL(a__sqr(mark(z063))) + MARK(1 + z063) :|: z063 >= 0, z = 1 + (1 + z063) A__DBL(z) -{ 1 }-> 1 + A__DBL(a__half(mark(z067))) + MARK(1 + z067) :|: z = 1 + (1 + z067), z067 >= 0 A__DBL(z) -{ 1 }-> 1 + A__DBL(a__first(mark(z066), mark(z121))) + MARK(1 + z066 + z121) :|: z = 1 + (1 + z066 + z121), z121 >= 0, z066 >= 0 A__DBL(z) -{ 1 }-> 1 + A__DBL(a__dbl(mark(z065))) + MARK(1 + z065) :|: z = 1 + (1 + z065), z065 >= 0 A__DBL(z) -{ 1 }-> 1 + A__DBL(a__add(mark(z064), mark(z120))) + MARK(1 + z064 + z120) :|: z120 >= 0, z = 1 + (1 + z064 + z120), z064 >= 0 A__DBL(z) -{ 1 }-> 1 + A__DBL(1) + MARK(1) :|: z = 1 + 1 A__DBL(z) -{ 1 }-> 1 + A__DBL(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 A__DBL(z) -{ 1 }-> 1 + A__DBL(0) + MARK(0) :|: z = 1 + 0 A__DBL(z) -{ 1 }-> 1 + A__DBL(1 + mark(z069)) + MARK(1 + z069) :|: z = 1 + (1 + z069), z069 >= 0 A__DBL(z) -{ 1 }-> 1 + A__DBL(1 + mark(z070)) + MARK(1 + z070) :|: z = 1 + (1 + z070), z070 >= 0 A__DBL(z) -{ 1 }-> 1 + A__DBL(1 + mark(z068) + z122) + MARK(1 + z068 + z122) :|: z122 >= 0, z = 1 + (1 + z068 + z122), z068 >= 0 A__FIRST(z, z') -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 A__HALF(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 A__HALF(z) -{ 1 }-> 1 + A__HALF(a__terms(mark(z0305))) + MARK(1 + z0305) :|: z = 1 + (1 + (1 + z0305)), z0305 >= 0 A__HALF(z) -{ 1 }-> 1 + A__HALF(a__sqr(mark(z0306))) + MARK(1 + z0306) :|: z0306 >= 0, z = 1 + (1 + (1 + z0306)) A__HALF(z) -{ 1 }-> 1 + A__HALF(a__half(mark(z0310))) + MARK(1 + z0310) :|: z0310 >= 0, z = 1 + (1 + (1 + z0310)) A__HALF(z) -{ 1 }-> 1 + A__HALF(a__first(mark(z0309), mark(z1102))) + MARK(1 + z0309 + z1102) :|: z0309 >= 0, z = 1 + (1 + (1 + z0309 + z1102)), z1102 >= 0 A__HALF(z) -{ 1 }-> 1 + A__HALF(a__dbl(mark(z0308))) + MARK(1 + z0308) :|: z0308 >= 0, z = 1 + (1 + (1 + z0308)) A__HALF(z) -{ 1 }-> 1 + A__HALF(a__add(mark(z0307), mark(z1101))) + MARK(1 + z0307 + z1101) :|: z = 1 + (1 + (1 + z0307 + z1101)), z0307 >= 0, z1101 >= 0 A__HALF(z) -{ 1 }-> 1 + A__HALF(1) + MARK(1) :|: z = 1 + (1 + 1) A__HALF(z) -{ 1 }-> 1 + A__HALF(0) + MARK(z0) :|: z0 >= 0, z = 1 + (1 + z0) A__HALF(z) -{ 1 }-> 1 + A__HALF(0) + MARK(0) :|: z = 1 + (1 + 0) A__HALF(z) -{ 1 }-> 1 + A__HALF(1 + mark(z0312)) + MARK(1 + z0312) :|: z = 1 + (1 + (1 + z0312)), z0312 >= 0 A__HALF(z) -{ 1 }-> 1 + A__HALF(1 + mark(z0313)) + MARK(1 + z0313) :|: z0313 >= 0, z = 1 + (1 + (1 + z0313)) A__HALF(z) -{ 1 }-> 1 + A__HALF(1 + mark(z0311) + z1103) + MARK(1 + z0311 + z1103) :|: z = 1 + (1 + (1 + z0311 + z1103)), z1103 >= 0, z0311 >= 0 A__SQR(z) -{ 1 }-> 1 + A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))) + A__SQR(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 A__SQR(z) -{ 1 }-> 1 + A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))) + A__DBL(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 A__TERMS(z) -{ 1 }-> 1 + A__SQR(a__terms(mark(z0'))) + MARK(1 + z0') :|: z0' >= 0, z = 1 + z0' A__TERMS(z) -{ 1 }-> 1 + A__SQR(a__sqr(mark(z0''))) + MARK(1 + z0'') :|: z0'' >= 0, z = 1 + z0'' A__TERMS(z) -{ 1 }-> 1 + A__SQR(a__half(mark(z04))) + MARK(1 + z04) :|: z04 >= 0, z = 1 + z04 A__TERMS(z) -{ 1 }-> 1 + A__SQR(a__first(mark(z03), mark(z1''))) + MARK(1 + z03 + z1'') :|: z = 1 + z03 + z1'', z03 >= 0, z1'' >= 0 A__TERMS(z) -{ 1 }-> 1 + A__SQR(a__dbl(mark(z02))) + MARK(1 + z02) :|: z = 1 + z02, z02 >= 0 A__TERMS(z) -{ 1 }-> 1 + A__SQR(a__add(mark(z01), mark(z1'))) + MARK(1 + z01 + z1') :|: z01 >= 0, z1' >= 0, z = 1 + z01 + z1' A__TERMS(z) -{ 1 }-> 1 + A__SQR(1) + MARK(1) :|: z = 1 A__TERMS(z) -{ 1 }-> 1 + A__SQR(0) + MARK(z0) :|: z = z0, z0 >= 0 A__TERMS(z) -{ 1 }-> 1 + A__SQR(0) + MARK(0) :|: z = 0 A__TERMS(z) -{ 1 }-> 1 + A__SQR(1 + mark(z06)) + MARK(1 + z06) :|: z06 >= 0, z = 1 + z06 A__TERMS(z) -{ 1 }-> 1 + A__SQR(1 + mark(z07)) + MARK(1 + z07) :|: z07 >= 0, z = 1 + z07 A__TERMS(z) -{ 1 }-> 1 + A__SQR(1 + mark(z05) + z11) + MARK(1 + z05 + z11) :|: z11 >= 0, z = 1 + z05 + z11, z05 >= 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(z0314))) + MARK(1 + z0314) :|: z0314 >= 0, z = 1 + (1 + z0314) MARK(z) -{ 1 }-> 1 + A__TERMS(a__sqr(mark(z0315))) + MARK(1 + z0315) :|: z = 1 + (1 + z0315), z0315 >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(a__half(mark(z0319))) + MARK(1 + z0319) :|: z0319 >= 0, z = 1 + (1 + z0319) MARK(z) -{ 1 }-> 1 + A__TERMS(a__first(mark(z0318), mark(z1105))) + MARK(1 + z0318 + z1105) :|: z0318 >= 0, z1105 >= 0, z = 1 + (1 + z0318 + z1105) MARK(z) -{ 1 }-> 1 + A__TERMS(a__dbl(mark(z0317))) + MARK(1 + z0317) :|: z = 1 + (1 + z0317), z0317 >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(a__add(mark(z0316), mark(z1104))) + MARK(1 + z0316 + z1104) :|: z0316 >= 0, z1104 >= 0, z = 1 + (1 + z0316 + z1104) 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 + mark(z0321)) + MARK(1 + z0321) :|: z = 1 + (1 + z0321), z0321 >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(1 + mark(z0322)) + MARK(1 + z0322) :|: z = 1 + (1 + z0322), z0322 >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(1 + mark(z0320) + z1106) + MARK(1 + z0320 + z1106) :|: z1106 >= 0, z0320 >= 0, z = 1 + (1 + z0320 + z1106) MARK(z) -{ 1 }-> 1 + A__SQR(a__terms(mark(z0323))) + MARK(1 + z0323) :|: z = 1 + (1 + z0323), z0323 >= 0 MARK(z) -{ 1 }-> 1 + A__SQR(a__sqr(mark(z0324))) + MARK(1 + z0324) :|: z = 1 + (1 + z0324), z0324 >= 0 MARK(z) -{ 1 }-> 1 + A__SQR(a__half(mark(z0328))) + MARK(1 + z0328) :|: z0328 >= 0, z = 1 + (1 + z0328) MARK(z) -{ 1 }-> 1 + A__SQR(a__first(mark(z0327), mark(z1108))) + MARK(1 + z0327 + z1108) :|: z = 1 + (1 + z0327 + z1108), z0327 >= 0, z1108 >= 0 MARK(z) -{ 1 }-> 1 + A__SQR(a__dbl(mark(z0326))) + MARK(1 + z0326) :|: z0326 >= 0, z = 1 + (1 + z0326) MARK(z) -{ 1 }-> 1 + A__SQR(a__add(mark(z0325), mark(z1107))) + MARK(1 + z0325 + z1107) :|: z = 1 + (1 + z0325 + z1107), z1107 >= 0, z0325 >= 0 MARK(z) -{ 1 }-> 1 + A__SQR(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__SQR(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__SQR(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__SQR(1 + mark(z0330)) + MARK(1 + z0330) :|: z0330 >= 0, z = 1 + (1 + z0330) MARK(z) -{ 1 }-> 1 + A__SQR(1 + mark(z0331)) + MARK(1 + z0331) :|: z0331 >= 0, z = 1 + (1 + z0331) MARK(z) -{ 1 }-> 1 + A__SQR(1 + mark(z0329) + z1109) + MARK(1 + z0329 + z1109) :|: z = 1 + (1 + z0329 + z1109), z0329 >= 0, z1109 >= 0 MARK(z) -{ 1 }-> 1 + A__HALF(a__terms(mark(z0809))) + MARK(1 + z0809) :|: z0809 >= 0, z = 1 + (1 + z0809) MARK(z) -{ 1 }-> 1 + A__HALF(a__sqr(mark(z0810))) + MARK(1 + z0810) :|: z = 1 + (1 + z0810), z0810 >= 0 MARK(z) -{ 1 }-> 1 + A__HALF(a__half(mark(z0814))) + MARK(1 + z0814) :|: z0814 >= 0, z = 1 + (1 + z0814) MARK(z) -{ 1 }-> 1 + A__HALF(a__first(mark(z0813), mark(z1270))) + MARK(1 + z0813 + z1270) :|: z0813 >= 0, z = 1 + (1 + z0813 + z1270), z1270 >= 0 MARK(z) -{ 1 }-> 1 + A__HALF(a__dbl(mark(z0812))) + MARK(1 + z0812) :|: z = 1 + (1 + z0812), z0812 >= 0 MARK(z) -{ 1 }-> 1 + A__HALF(a__add(mark(z0811), mark(z1269))) + MARK(1 + z0811 + z1269) :|: z = 1 + (1 + z0811 + z1269), z1269 >= 0, z0811 >= 0 MARK(z) -{ 1 }-> 1 + A__HALF(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__HALF(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__HALF(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__HALF(1 + mark(z0816)) + MARK(1 + z0816) :|: z = 1 + (1 + z0816), z0816 >= 0 MARK(z) -{ 1 }-> 1 + A__HALF(1 + mark(z0817)) + MARK(1 + z0817) :|: z = 1 + (1 + z0817), z0817 >= 0 MARK(z) -{ 1 }-> 1 + A__HALF(1 + mark(z0815) + z1271) + MARK(1 + z0815 + z1271) :|: z1271 >= 0, z = 1 + (1 + z0815 + z1271), z0815 >= 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__DBL(a__terms(mark(z0566))) + MARK(1 + z0566) :|: z = 1 + (1 + z0566), z0566 >= 0 MARK(z) -{ 1 }-> 1 + A__DBL(a__sqr(mark(z0567))) + MARK(1 + z0567) :|: z0567 >= 0, z = 1 + (1 + z0567) MARK(z) -{ 1 }-> 1 + A__DBL(a__half(mark(z0571))) + MARK(1 + z0571) :|: z = 1 + (1 + z0571), z0571 >= 0 MARK(z) -{ 1 }-> 1 + A__DBL(a__first(mark(z0570), mark(z1189))) + MARK(1 + z0570 + z1189) :|: z0570 >= 0, z = 1 + (1 + z0570 + z1189), z1189 >= 0 MARK(z) -{ 1 }-> 1 + A__DBL(a__dbl(mark(z0569))) + MARK(1 + z0569) :|: z = 1 + (1 + z0569), z0569 >= 0 MARK(z) -{ 1 }-> 1 + A__DBL(a__add(mark(z0568), mark(z1188))) + MARK(1 + z0568 + z1188) :|: z = 1 + (1 + z0568 + z1188), z0568 >= 0, z1188 >= 0 MARK(z) -{ 1 }-> 1 + A__DBL(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__DBL(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__DBL(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__DBL(1 + mark(z0573)) + MARK(1 + z0573) :|: z0573 >= 0, z = 1 + (1 + z0573) MARK(z) -{ 1 }-> 1 + A__DBL(1 + mark(z0574)) + MARK(1 + z0574) :|: z = 1 + (1 + z0574), z0574 >= 0 MARK(z) -{ 1 }-> 1 + A__DBL(1 + mark(z0572) + z1190) + MARK(1 + z0572 + z1190) :|: z = 1 + (1 + z0572 + z1190), z0572 >= 0, z1190 >= 0 MARK(z) -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__add(z, z') -{ 0 }-> mark(z0) :|: z0 >= 0, z = 0, z' = z0 a__add(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__add(z, z') -{ 0 }-> 1 + a__add(mark(z0), mark(z1)) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 a__add(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__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 + a__dbl(a__terms(mark(z0845)))) :|: z = 1 + (1 + z0845), z0845 >= 0 a__dbl(z) -{ 0 }-> 1 + (1 + a__dbl(a__sqr(mark(z0846)))) :|: z = 1 + (1 + z0846), z0846 >= 0 a__dbl(z) -{ 0 }-> 1 + (1 + a__dbl(a__half(mark(z0850)))) :|: z0850 >= 0, z = 1 + (1 + z0850) a__dbl(z) -{ 0 }-> 1 + (1 + a__dbl(a__first(mark(z0849), mark(z1282)))) :|: z = 1 + (1 + z0849 + z1282), z1282 >= 0, z0849 >= 0 a__dbl(z) -{ 0 }-> 1 + (1 + a__dbl(a__dbl(mark(z0848)))) :|: z = 1 + (1 + z0848), z0848 >= 0 a__dbl(z) -{ 0 }-> 1 + (1 + a__dbl(a__add(mark(z0847), mark(z1281)))) :|: z1281 >= 0, z0847 >= 0, z = 1 + (1 + z0847 + z1281) a__dbl(z) -{ 0 }-> 1 + (1 + a__dbl(1)) :|: z = 1 + 1 a__dbl(z) -{ 0 }-> 1 + (1 + a__dbl(0)) :|: z = 1 + 0 a__dbl(z) -{ 0 }-> 1 + (1 + a__dbl(0)) :|: z = 1 + z0, z0 >= 0 a__dbl(z) -{ 0 }-> 1 + (1 + a__dbl(1 + mark(z0852))) :|: z0852 >= 0, z = 1 + (1 + z0852) a__dbl(z) -{ 0 }-> 1 + (1 + a__dbl(1 + mark(z0853))) :|: z0853 >= 0, z = 1 + (1 + z0853) a__dbl(z) -{ 0 }-> 1 + (1 + a__dbl(1 + mark(z0851) + z1283)) :|: z0851 >= 0, z1283 >= 0, z = 1 + (1 + z0851 + z1283) 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__half(z) -{ 0 }-> mark(z0) :|: z = 1 + z0, z0 >= 0 a__half(z) -{ 0 }-> 0 :|: z = 0 a__half(z) -{ 0 }-> 0 :|: z = 1 + 0 a__half(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__half(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__half(z) -{ 0 }-> 1 + a__half(a__terms(mark(z0971))) :|: z = 1 + (1 + (1 + z0971)), z0971 >= 0 a__half(z) -{ 0 }-> 1 + a__half(a__sqr(mark(z0972))) :|: z = 1 + (1 + (1 + z0972)), z0972 >= 0 a__half(z) -{ 0 }-> 1 + a__half(a__half(mark(z0976))) :|: z0976 >= 0, z = 1 + (1 + (1 + z0976)) a__half(z) -{ 0 }-> 1 + a__half(a__first(mark(z0975), mark(z1324))) :|: z0975 >= 0, z1324 >= 0, z = 1 + (1 + (1 + z0975 + z1324)) a__half(z) -{ 0 }-> 1 + a__half(a__dbl(mark(z0974))) :|: z = 1 + (1 + (1 + z0974)), z0974 >= 0 a__half(z) -{ 0 }-> 1 + a__half(a__add(mark(z0973), mark(z1323))) :|: z0973 >= 0, z1323 >= 0, z = 1 + (1 + (1 + z0973 + z1323)) a__half(z) -{ 0 }-> 1 + a__half(1) :|: z = 1 + (1 + 1) a__half(z) -{ 0 }-> 1 + a__half(0) :|: z = 1 + (1 + 0) a__half(z) -{ 0 }-> 1 + a__half(0) :|: z0 >= 0, z = 1 + (1 + z0) a__half(z) -{ 0 }-> 1 + a__half(1 + mark(z0978)) :|: z0978 >= 0, z = 1 + (1 + (1 + z0978)) a__half(z) -{ 0 }-> 1 + a__half(1 + mark(z0979)) :|: z0979 >= 0, z = 1 + (1 + (1 + z0979)) a__half(z) -{ 0 }-> 1 + a__half(1 + mark(z0977) + z1325) :|: z = 1 + (1 + (1 + z0977 + z1325)), z0977 >= 0, z1325 >= 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 + a__add(a__sqr(mark(z0)), a__dbl(mark(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(z0818)))) + (1 + (1 + (1 + z0818))) :|: z = 1 + z0818, z0818 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(a__sqr(mark(z0819)))) + (1 + (1 + (1 + z0819))) :|: z = 1 + z0819, z0819 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(a__half(mark(z0823)))) + (1 + (1 + (1 + z0823))) :|: z0823 >= 0, z = 1 + z0823 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(a__first(mark(z0822), mark(z1273)))) + (1 + (1 + (1 + z0822 + z1273))) :|: z0822 >= 0, z = 1 + z0822 + z1273, z1273 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(a__dbl(mark(z0821)))) + (1 + (1 + (1 + z0821))) :|: z0821 >= 0, z = 1 + z0821 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(a__add(mark(z0820), mark(z1272)))) + (1 + (1 + (1 + z0820 + z1272))) :|: z1272 >= 0, z0820 >= 0, z = 1 + z0820 + z1272 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 + mark(z0825))) + (1 + (1 + (1 + z0825))) :|: z = 1 + z0825, z0825 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(1 + mark(z0826))) + (1 + (1 + (1 + z0826))) :|: z0826 >= 0, z = 1 + z0826 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(1 + mark(z0824) + z1274)) + (1 + (1 + (1 + z0824 + z1274))) :|: z1274 >= 0, z0824 >= 0, z = 1 + z0824 + z1274 mark(z) -{ 0 }-> a__terms(a__terms(mark(z0980))) :|: z = 1 + (1 + z0980), z0980 >= 0 mark(z) -{ 0 }-> a__terms(a__sqr(mark(z0981))) :|: z = 1 + (1 + z0981), z0981 >= 0 mark(z) -{ 0 }-> a__terms(a__half(mark(z0985))) :|: z = 1 + (1 + z0985), z0985 >= 0 mark(z) -{ 0 }-> a__terms(a__first(mark(z0984), mark(z1327))) :|: z1327 >= 0, z = 1 + (1 + z0984 + z1327), z0984 >= 0 mark(z) -{ 0 }-> a__terms(a__dbl(mark(z0983))) :|: z = 1 + (1 + z0983), z0983 >= 0 mark(z) -{ 0 }-> a__terms(a__add(mark(z0982), mark(z1326))) :|: z = 1 + (1 + z0982 + z1326), z0982 >= 0, z1326 >= 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 + mark(z0987)) :|: z = 1 + (1 + z0987), z0987 >= 0 mark(z) -{ 0 }-> a__terms(1 + mark(z0988)) :|: z0988 >= 0, z = 1 + (1 + z0988) mark(z) -{ 0 }-> a__terms(1 + mark(z0986) + z1328) :|: z = 1 + (1 + z0986 + z1328), z0986 >= 0, z1328 >= 0 mark(z) -{ 0 }-> a__sqr(a__terms(mark(z0989))) :|: z = 1 + (1 + z0989), z0989 >= 0 mark(z) -{ 0 }-> a__sqr(a__sqr(mark(z0990))) :|: z = 1 + (1 + z0990), z0990 >= 0 mark(z) -{ 0 }-> a__sqr(a__half(mark(z0994))) :|: z = 1 + (1 + z0994), z0994 >= 0 mark(z) -{ 0 }-> a__sqr(a__first(mark(z0993), mark(z1330))) :|: z1330 >= 0, z0993 >= 0, z = 1 + (1 + z0993 + z1330) mark(z) -{ 0 }-> a__sqr(a__dbl(mark(z0992))) :|: z = 1 + (1 + z0992), z0992 >= 0 mark(z) -{ 0 }-> a__sqr(a__add(mark(z0991), mark(z1329))) :|: z = 1 + (1 + z0991 + z1329), z1329 >= 0, z0991 >= 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 + mark(z0996)) :|: z0996 >= 0, z = 1 + (1 + z0996) mark(z) -{ 0 }-> a__sqr(1 + mark(z0997)) :|: z0997 >= 0, z = 1 + (1 + z0997) mark(z) -{ 0 }-> a__sqr(1 + mark(z0995) + z1331) :|: z1331 >= 0, z = 1 + (1 + z0995 + z1331), z0995 >= 0 mark(z) -{ 0 }-> a__half(a__terms(mark(z01241))) :|: z = 1 + (1 + z01241), z01241 >= 0 mark(z) -{ 0 }-> a__half(a__sqr(mark(z01242))) :|: z = 1 + (1 + z01242), z01242 >= 0 mark(z) -{ 0 }-> a__half(a__half(mark(z01246))) :|: z = 1 + (1 + z01246), z01246 >= 0 mark(z) -{ 0 }-> a__half(a__first(mark(z01245), mark(z1414))) :|: z1414 >= 0, z = 1 + (1 + z01245 + z1414), z01245 >= 0 mark(z) -{ 0 }-> a__half(a__dbl(mark(z01244))) :|: z01244 >= 0, z = 1 + (1 + z01244) mark(z) -{ 0 }-> a__half(a__add(mark(z01243), mark(z1413))) :|: z1413 >= 0, z = 1 + (1 + z01243 + z1413), z01243 >= 0 mark(z) -{ 0 }-> a__half(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__half(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__half(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__half(1 + mark(z01248)) :|: z01248 >= 0, z = 1 + (1 + z01248) mark(z) -{ 0 }-> a__half(1 + mark(z01249)) :|: z01249 >= 0, z = 1 + (1 + z01249) mark(z) -{ 0 }-> a__half(1 + mark(z01247) + z1415) :|: z = 1 + (1 + z01247 + z1415), z01247 >= 0, z1415 >= 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(z01115))) :|: z = 1 + (1 + z01115), z01115 >= 0 mark(z) -{ 0 }-> a__dbl(a__sqr(mark(z01116))) :|: z = 1 + (1 + z01116), z01116 >= 0 mark(z) -{ 0 }-> a__dbl(a__half(mark(z01120))) :|: z01120 >= 0, z = 1 + (1 + z01120) mark(z) -{ 0 }-> a__dbl(a__first(mark(z01119), mark(z1372))) :|: z01119 >= 0, z1372 >= 0, z = 1 + (1 + z01119 + z1372) mark(z) -{ 0 }-> a__dbl(a__dbl(mark(z01118))) :|: z = 1 + (1 + z01118), z01118 >= 0 mark(z) -{ 0 }-> a__dbl(a__add(mark(z01117), mark(z1371))) :|: z1371 >= 0, z = 1 + (1 + z01117 + z1371), z01117 >= 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 + mark(z01122)) :|: z = 1 + (1 + z01122), z01122 >= 0 mark(z) -{ 0 }-> a__dbl(1 + mark(z01123)) :|: z = 1 + (1 + z01123), z01123 >= 0 mark(z) -{ 0 }-> a__dbl(1 + mark(z01121) + z1373) :|: z01121 >= 0, z1373 >= 0, z = 1 + (1 + z01121 + z1373) 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 + mark(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ---------------------------------------- (63) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (64) Obligation: Complexity RNTS consisting of the following rules: A__ADD(z, z') -{ 1 }-> 1 + MARK(z') :|: z' >= 0, z = 0 A__ADD(z, z') -{ 1 }-> 1 + A__ADD(mark(z - 1), mark(z')) + MARK(z') :|: z' >= 0, z - 1 >= 0 A__ADD(z, z') -{ 1 }-> 1 + A__ADD(mark(z - 1), mark(z')) + MARK(z - 1) :|: z' >= 0, z - 1 >= 0 A__DBL(z) -{ 1 }-> 1 + A__DBL(a__terms(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 A__DBL(z) -{ 1 }-> 1 + A__DBL(a__sqr(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 A__DBL(z) -{ 1 }-> 1 + A__DBL(a__half(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 A__DBL(z) -{ 1 }-> 1 + A__DBL(a__first(mark(z066), mark(z121))) + MARK(1 + z066 + z121) :|: z = 1 + (1 + z066 + z121), z121 >= 0, z066 >= 0 A__DBL(z) -{ 1 }-> 1 + A__DBL(a__dbl(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 A__DBL(z) -{ 1 }-> 1 + A__DBL(a__add(mark(z064), mark(z120))) + MARK(1 + z064 + z120) :|: z120 >= 0, z = 1 + (1 + z064 + z120), z064 >= 0 A__DBL(z) -{ 1 }-> 1 + A__DBL(1) + MARK(1) :|: z = 1 + 1 A__DBL(z) -{ 1 }-> 1 + A__DBL(0) + MARK(0) :|: z = 1 + 0 A__DBL(z) -{ 1 }-> 1 + A__DBL(0) + MARK(z - 1) :|: z - 1 >= 0 A__DBL(z) -{ 1 }-> 1 + A__DBL(1 + mark(z - 2)) + MARK(1 + (z - 2)) :|: z - 2 >= 0 A__DBL(z) -{ 1 }-> 1 + A__DBL(1 + mark(z068) + z122) + MARK(1 + z068 + z122) :|: z122 >= 0, z = 1 + (1 + z068 + z122), z068 >= 0 A__FIRST(z, z') -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 A__HALF(z) -{ 1 }-> 1 + MARK(z - 1) :|: z - 1 >= 0 A__HALF(z) -{ 1 }-> 1 + A__HALF(a__terms(mark(z - 3))) + MARK(1 + (z - 3)) :|: z - 3 >= 0 A__HALF(z) -{ 1 }-> 1 + A__HALF(a__sqr(mark(z - 3))) + MARK(1 + (z - 3)) :|: z - 3 >= 0 A__HALF(z) -{ 1 }-> 1 + A__HALF(a__half(mark(z - 3))) + MARK(1 + (z - 3)) :|: z - 3 >= 0 A__HALF(z) -{ 1 }-> 1 + A__HALF(a__first(mark(z0309), mark(z1102))) + MARK(1 + z0309 + z1102) :|: z0309 >= 0, z = 1 + (1 + (1 + z0309 + z1102)), z1102 >= 0 A__HALF(z) -{ 1 }-> 1 + A__HALF(a__dbl(mark(z - 3))) + MARK(1 + (z - 3)) :|: z - 3 >= 0 A__HALF(z) -{ 1 }-> 1 + A__HALF(a__add(mark(z0307), mark(z1101))) + MARK(1 + z0307 + z1101) :|: z = 1 + (1 + (1 + z0307 + z1101)), z0307 >= 0, z1101 >= 0 A__HALF(z) -{ 1 }-> 1 + A__HALF(1) + MARK(1) :|: z = 1 + (1 + 1) A__HALF(z) -{ 1 }-> 1 + A__HALF(0) + MARK(0) :|: z = 1 + (1 + 0) A__HALF(z) -{ 1 }-> 1 + A__HALF(0) + MARK(z - 2) :|: z - 2 >= 0 A__HALF(z) -{ 1 }-> 1 + A__HALF(1 + mark(z - 3)) + MARK(1 + (z - 3)) :|: z - 3 >= 0 A__HALF(z) -{ 1 }-> 1 + A__HALF(1 + mark(z0311) + z1103) + MARK(1 + z0311 + z1103) :|: z = 1 + (1 + (1 + z0311 + z1103)), z1103 >= 0, z0311 >= 0 A__SQR(z) -{ 1 }-> 1 + A__ADD(a__sqr(mark(z - 1)), a__dbl(mark(z - 1))) + A__SQR(mark(z - 1)) + MARK(z - 1) :|: z - 1 >= 0 A__SQR(z) -{ 1 }-> 1 + A__ADD(a__sqr(mark(z - 1)), a__dbl(mark(z - 1))) + A__DBL(mark(z - 1)) + MARK(z - 1) :|: z - 1 >= 0 A__TERMS(z) -{ 1 }-> 1 + A__SQR(a__terms(mark(z - 1))) + MARK(1 + (z - 1)) :|: z - 1 >= 0 A__TERMS(z) -{ 1 }-> 1 + A__SQR(a__sqr(mark(z - 1))) + MARK(1 + (z - 1)) :|: z - 1 >= 0 A__TERMS(z) -{ 1 }-> 1 + A__SQR(a__half(mark(z - 1))) + MARK(1 + (z - 1)) :|: z - 1 >= 0 A__TERMS(z) -{ 1 }-> 1 + A__SQR(a__first(mark(z03), mark(z1''))) + MARK(1 + z03 + z1'') :|: z = 1 + z03 + z1'', z03 >= 0, z1'' >= 0 A__TERMS(z) -{ 1 }-> 1 + A__SQR(a__dbl(mark(z - 1))) + MARK(1 + (z - 1)) :|: z - 1 >= 0 A__TERMS(z) -{ 1 }-> 1 + A__SQR(a__add(mark(z01), mark(z1'))) + MARK(1 + z01 + z1') :|: z01 >= 0, z1' >= 0, z = 1 + z01 + z1' A__TERMS(z) -{ 1 }-> 1 + A__SQR(1) + MARK(1) :|: z = 1 A__TERMS(z) -{ 1 }-> 1 + A__SQR(0) + MARK(z) :|: z >= 0 A__TERMS(z) -{ 1 }-> 1 + A__SQR(0) + MARK(0) :|: z = 0 A__TERMS(z) -{ 1 }-> 1 + A__SQR(1 + mark(z - 1)) + MARK(1 + (z - 1)) :|: z - 1 >= 0 A__TERMS(z) -{ 1 }-> 1 + A__SQR(1 + mark(z05) + z11) + MARK(1 + z05 + z11) :|: z11 >= 0, z = 1 + z05 + z11, z05 >= 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__half(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(a__first(mark(z0318), mark(z1105))) + MARK(1 + z0318 + z1105) :|: z0318 >= 0, z1105 >= 0, z = 1 + (1 + z0318 + z1105) 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(z0316), mark(z1104))) + MARK(1 + z0316 + z1104) :|: z0316 >= 0, z1104 >= 0, z = 1 + (1 + z0316 + z1104) 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 + mark(z0320) + z1106) + MARK(1 + z0320 + z1106) :|: z1106 >= 0, z0320 >= 0, z = 1 + (1 + z0320 + z1106) MARK(z) -{ 1 }-> 1 + A__SQR(a__terms(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__SQR(a__sqr(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__SQR(a__half(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__SQR(a__first(mark(z0327), mark(z1108))) + MARK(1 + z0327 + z1108) :|: z = 1 + (1 + z0327 + z1108), z0327 >= 0, z1108 >= 0 MARK(z) -{ 1 }-> 1 + A__SQR(a__dbl(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__SQR(a__add(mark(z0325), mark(z1107))) + MARK(1 + z0325 + z1107) :|: z = 1 + (1 + z0325 + z1107), z1107 >= 0, z0325 >= 0 MARK(z) -{ 1 }-> 1 + A__SQR(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__SQR(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__SQR(0) + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__SQR(1 + mark(z - 2)) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__SQR(1 + mark(z0329) + z1109) + MARK(1 + z0329 + z1109) :|: z = 1 + (1 + z0329 + z1109), z0329 >= 0, z1109 >= 0 MARK(z) -{ 1 }-> 1 + A__HALF(a__terms(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__HALF(a__sqr(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__HALF(a__half(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__HALF(a__first(mark(z0813), mark(z1270))) + MARK(1 + z0813 + z1270) :|: z0813 >= 0, z = 1 + (1 + z0813 + z1270), z1270 >= 0 MARK(z) -{ 1 }-> 1 + A__HALF(a__dbl(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__HALF(a__add(mark(z0811), mark(z1269))) + MARK(1 + z0811 + z1269) :|: z = 1 + (1 + z0811 + z1269), z1269 >= 0, z0811 >= 0 MARK(z) -{ 1 }-> 1 + A__HALF(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__HALF(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__HALF(0) + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__HALF(1 + mark(z - 2)) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__HALF(1 + mark(z0815) + z1271) + MARK(1 + z0815 + z1271) :|: z1271 >= 0, z = 1 + (1 + z0815 + z1271), z0815 >= 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__DBL(a__terms(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__DBL(a__sqr(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__DBL(a__half(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__DBL(a__first(mark(z0570), mark(z1189))) + MARK(1 + z0570 + z1189) :|: z0570 >= 0, z = 1 + (1 + z0570 + z1189), z1189 >= 0 MARK(z) -{ 1 }-> 1 + A__DBL(a__dbl(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__DBL(a__add(mark(z0568), mark(z1188))) + MARK(1 + z0568 + z1188) :|: z = 1 + (1 + z0568 + z1188), z0568 >= 0, z1188 >= 0 MARK(z) -{ 1 }-> 1 + A__DBL(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__DBL(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__DBL(0) + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__DBL(1 + mark(z - 2)) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__DBL(1 + mark(z0572) + z1190) + MARK(1 + z0572 + z1190) :|: z = 1 + (1 + z0572 + z1190), z0572 >= 0, z1190 >= 0 MARK(z) -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__add(z, z') -{ 0 }-> mark(z') :|: z' >= 0, z = 0 a__add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__add(z, z') -{ 0 }-> 1 + a__add(mark(z - 1), mark(z')) :|: z' >= 0, z - 1 >= 0 a__add(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__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 + a__dbl(a__terms(mark(z - 2)))) :|: z - 2 >= 0 a__dbl(z) -{ 0 }-> 1 + (1 + a__dbl(a__sqr(mark(z - 2)))) :|: z - 2 >= 0 a__dbl(z) -{ 0 }-> 1 + (1 + a__dbl(a__half(mark(z - 2)))) :|: z - 2 >= 0 a__dbl(z) -{ 0 }-> 1 + (1 + a__dbl(a__first(mark(z0849), mark(z1282)))) :|: z = 1 + (1 + z0849 + z1282), z1282 >= 0, z0849 >= 0 a__dbl(z) -{ 0 }-> 1 + (1 + a__dbl(a__dbl(mark(z - 2)))) :|: z - 2 >= 0 a__dbl(z) -{ 0 }-> 1 + (1 + a__dbl(a__add(mark(z0847), mark(z1281)))) :|: z1281 >= 0, z0847 >= 0, z = 1 + (1 + z0847 + z1281) a__dbl(z) -{ 0 }-> 1 + (1 + a__dbl(1)) :|: z = 1 + 1 a__dbl(z) -{ 0 }-> 1 + (1 + a__dbl(0)) :|: z = 1 + 0 a__dbl(z) -{ 0 }-> 1 + (1 + a__dbl(0)) :|: z - 1 >= 0 a__dbl(z) -{ 0 }-> 1 + (1 + a__dbl(1 + mark(z - 2))) :|: z - 2 >= 0 a__dbl(z) -{ 0 }-> 1 + (1 + a__dbl(1 + mark(z0851) + z1283)) :|: z0851 >= 0, z1283 >= 0, z = 1 + (1 + z0851 + z1283) 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__half(z) -{ 0 }-> mark(z - 1) :|: z - 1 >= 0 a__half(z) -{ 0 }-> 0 :|: z = 0 a__half(z) -{ 0 }-> 0 :|: z = 1 + 0 a__half(z) -{ 0 }-> 0 :|: z >= 0 a__half(z) -{ 0 }-> 1 + z :|: z >= 0 a__half(z) -{ 0 }-> 1 + a__half(a__terms(mark(z - 3))) :|: z - 3 >= 0 a__half(z) -{ 0 }-> 1 + a__half(a__sqr(mark(z - 3))) :|: z - 3 >= 0 a__half(z) -{ 0 }-> 1 + a__half(a__half(mark(z - 3))) :|: z - 3 >= 0 a__half(z) -{ 0 }-> 1 + a__half(a__first(mark(z0975), mark(z1324))) :|: z0975 >= 0, z1324 >= 0, z = 1 + (1 + (1 + z0975 + z1324)) a__half(z) -{ 0 }-> 1 + a__half(a__dbl(mark(z - 3))) :|: z - 3 >= 0 a__half(z) -{ 0 }-> 1 + a__half(a__add(mark(z0973), mark(z1323))) :|: z0973 >= 0, z1323 >= 0, z = 1 + (1 + (1 + z0973 + z1323)) a__half(z) -{ 0 }-> 1 + a__half(1) :|: z = 1 + (1 + 1) a__half(z) -{ 0 }-> 1 + a__half(0) :|: z = 1 + (1 + 0) a__half(z) -{ 0 }-> 1 + a__half(0) :|: z - 2 >= 0 a__half(z) -{ 0 }-> 1 + a__half(1 + mark(z - 3)) :|: z - 3 >= 0 a__half(z) -{ 0 }-> 1 + a__half(1 + mark(z0977) + z1325) :|: z = 1 + (1 + (1 + z0977 + z1325)), z0977 >= 0, z1325 >= 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 + a__add(a__sqr(mark(z - 1)), a__dbl(mark(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__half(mark(z - 1)))) + (1 + (1 + (1 + (z - 1)))) :|: z - 1 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(a__first(mark(z0822), mark(z1273)))) + (1 + (1 + (1 + z0822 + z1273))) :|: z0822 >= 0, z = 1 + z0822 + z1273, z1273 >= 0 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(z0820), mark(z1272)))) + (1 + (1 + (1 + z0820 + z1272))) :|: z1272 >= 0, z0820 >= 0, z = 1 + z0820 + z1272 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 + z)) :|: z >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(0)) + (1 + (1 + 0)) :|: z = 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(z0824) + z1274)) + (1 + (1 + (1 + z0824 + z1274))) :|: z1274 >= 0, z0824 >= 0, z = 1 + z0824 + z1274 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__half(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__terms(a__first(mark(z0984), mark(z1327))) :|: z1327 >= 0, z = 1 + (1 + z0984 + z1327), z0984 >= 0 mark(z) -{ 0 }-> a__terms(a__dbl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__terms(a__add(mark(z0982), mark(z1326))) :|: z = 1 + (1 + z0982 + z1326), z0982 >= 0, z1326 >= 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 + mark(z0986) + z1328) :|: z = 1 + (1 + z0986 + z1328), z0986 >= 0, z1328 >= 0 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__half(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__sqr(a__first(mark(z0993), mark(z1330))) :|: z1330 >= 0, z0993 >= 0, z = 1 + (1 + z0993 + z1330) mark(z) -{ 0 }-> a__sqr(a__dbl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__sqr(a__add(mark(z0991), mark(z1329))) :|: z = 1 + (1 + z0991 + z1329), z1329 >= 0, z0991 >= 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 >= 0 mark(z) -{ 0 }-> a__sqr(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__sqr(1 + mark(z0995) + z1331) :|: z1331 >= 0, z = 1 + (1 + z0995 + z1331), z0995 >= 0 mark(z) -{ 0 }-> a__half(a__terms(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__half(a__sqr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__half(a__half(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__half(a__first(mark(z01245), mark(z1414))) :|: z1414 >= 0, z = 1 + (1 + z01245 + z1414), z01245 >= 0 mark(z) -{ 0 }-> a__half(a__dbl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__half(a__add(mark(z01243), mark(z1413))) :|: z1413 >= 0, z = 1 + (1 + z01243 + z1413), z01243 >= 0 mark(z) -{ 0 }-> a__half(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__half(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__half(0) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__half(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__half(1 + mark(z01247) + z1415) :|: z = 1 + (1 + z01247 + z1415), z01247 >= 0, z1415 >= 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__half(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__dbl(a__first(mark(z01119), mark(z1372))) :|: z01119 >= 0, z1372 >= 0, z = 1 + (1 + z01119 + z1372) mark(z) -{ 0 }-> a__dbl(a__dbl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__dbl(a__add(mark(z01117), mark(z1371))) :|: z1371 >= 0, z = 1 + (1 + z01117 + z1371), z01117 >= 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 >= 0 mark(z) -{ 0 }-> a__dbl(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__dbl(1 + mark(z01121) + z1373) :|: z01121 >= 0, z1373 >= 0, z = 1 + (1 + z01121 + z1373) 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 }-> 1 + mark(z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ---------------------------------------- (65) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: a__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] a__half(v0) -> null_a__half [0] mark(v0) -> null_mark [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] A__HALF(v0) -> null_A__HALF [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_a__half, null_mark, null_A__SQR, null_A__DBL, null_A__ADD, null_A__FIRST, null_A__HALF, null_MARK, const ---------------------------------------- (66) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) [1] A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) [1] A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) [1] A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) [1] A__ADD(0, z0) -> c9(MARK(z0)) [1] A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) [1] A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) [1] A__HALF(dbl(z0)) -> c19(MARK(z0)) [1] MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) [1] MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) [1] MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) [1] MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) [1] MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) [1] MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) [1] MARK(cons(z0, z1)) -> c29(MARK(z0)) [1] MARK(recip(z0)) -> c30(MARK(z0)) [1] MARK(s(z0)) -> c31(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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) [0] a__sqr(z0) -> sqr(z0) [0] a__dbl(0) -> 0 [0] a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) [0] a__dbl(z0) -> dbl(z0) [0] a__add(0, z0) -> mark(z0) [0] a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) [0] a__add(z0, z1) -> add(z0, z1) [0] a__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] a__half(0) -> 0 [0] a__half(s(0)) -> 0 [0] a__half(s(s(z0))) -> s(a__half(mark(z0))) [0] a__half(dbl(z0)) -> mark(z0) [0] a__half(z0) -> half(z0) [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(half(z0)) -> a__half(mark(z0)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(recip(z0)) -> recip(mark(z0)) [0] mark(s(z0)) -> s(mark(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] a__half(v0) -> null_a__half [0] mark(v0) -> null_mark [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] A__HALF(v0) -> null_A__HALF [0] MARK(v0) -> null_MARK [0] The TRS has the following type information: A__TERMS :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> c c :: c3:c4:null_A__SQR -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK -> c A__SQR :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> c3:c4:null_A__SQR mark :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark MARK :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK s :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c3 :: c9:c10:c11:null_A__ADD -> c3:c4:null_A__SQR -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK -> c3:c4:null_A__SQR A__ADD :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> c9:c10:c11:null_A__ADD a__sqr :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark a__dbl :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c4 :: c9:c10:c11:null_A__ADD -> c7:null_A__DBL -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK -> c3:c4:null_A__SQR A__DBL :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> c7:null_A__DBL c7 :: c7:null_A__DBL -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK -> c7:null_A__DBL 0 :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c9 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK -> c9:c10:c11:null_A__ADD c10 :: c9:c10:c11:null_A__ADD -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK -> c9:c10:c11:null_A__ADD c11 :: c9:c10:c11:null_A__ADD -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK -> c9:c10:c11:null_A__ADD A__FIRST :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> c14:null_A__FIRST cons :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c14 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK -> c14:null_A__FIRST A__HALF :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> c18:c19:null_A__HALF c18 :: c18:c19:null_A__HALF -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK -> c18:c19:null_A__HALF dbl :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c19 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK -> c18:c19:null_A__HALF terms :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c21 :: c -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK sqr :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c22 :: c3:c4:null_A__SQR -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK add :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c23 :: c9:c10:c11:null_A__ADD -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK c24 :: c9:c10:c11:null_A__ADD -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK c25 :: c7:null_A__DBL -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK first :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c26 :: c14:null_A__FIRST -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK c27 :: c14:null_A__FIRST -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK half :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c28 :: c18:c19:null_A__HALF -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK c29 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK recip :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark c30 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK c31 :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK -> c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK a__terms :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark a__add :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark a__first :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark nil :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark a__half :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark -> s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark null_a__terms :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark null_a__sqr :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark null_a__dbl :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark null_a__add :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark null_a__first :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark null_a__half :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark null_mark :: s:0:cons:dbl:terms:sqr:add:first:half:recip:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_a__half:null_mark null_A__SQR :: c3:c4:null_A__SQR null_A__DBL :: c7:null_A__DBL null_A__ADD :: c9:c10:c11:null_A__ADD null_A__FIRST :: c14:null_A__FIRST null_A__HALF :: c18:c19:null_A__HALF null_MARK :: c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:null_MARK const :: c Rewrite Strategy: INNERMOST ---------------------------------------- (67) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 nil => 1 null_a__terms => 0 null_a__sqr => 0 null_a__dbl => 0 null_a__add => 0 null_a__first => 0 null_a__half => 0 null_mark => 0 null_A__SQR => 0 null_A__DBL => 0 null_A__ADD => 0 null_A__FIRST => 0 null_A__HALF => 0 null_MARK => 0 const => 0 ---------------------------------------- (68) Obligation: Complexity RNTS consisting of the following rules: A__ADD(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__ADD(z, z') -{ 1 }-> 1 + MARK(z0) :|: z0 >= 0, z = 0, z' = z0 A__ADD(z, z') -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 A__ADD(z, z') -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 A__DBL(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__DBL(z) -{ 1 }-> 1 + A__DBL(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 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__HALF(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__HALF(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 A__HALF(z) -{ 1 }-> 1 + A__HALF(mark(z0)) + MARK(z0) :|: z0 >= 0, z = 1 + (1 + z0) A__SQR(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__SQR(z) -{ 1 }-> 1 + A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))) + A__SQR(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 A__SQR(z) -{ 1 }-> 1 + A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))) + A__DBL(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 A__TERMS(z) -{ 1 }-> 1 + A__SQR(mark(z0)) + 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__SQR(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__HALF(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__DBL(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__add(z, z') -{ 0 }-> mark(z0) :|: z0 >= 0, z = 0, z' = z0 a__add(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__add(z, z') -{ 0 }-> 1 + a__add(mark(z0), mark(z1)) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 a__add(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__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 + a__dbl(mark(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__half(z) -{ 0 }-> mark(z0) :|: z = 1 + z0, z0 >= 0 a__half(z) -{ 0 }-> 0 :|: z = 0 a__half(z) -{ 0 }-> 0 :|: z = 1 + 0 a__half(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__half(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__half(z) -{ 0 }-> 1 + a__half(mark(z0)) :|: z0 >= 0, z = 1 + (1 + z0) 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 + a__add(a__sqr(mark(z0)), a__dbl(mark(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__half(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 + 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. ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) by A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(cons(z0, z1)) -> c(A__SQR(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(A__SQR(recip(mark(z0))), MARK(recip(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(0) -> c(A__SQR(0), MARK(0)) A__TERMS(nil) -> c(A__SQR(nil), MARK(nil)) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(cons(z0, z1)) -> c(A__SQR(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(A__SQR(recip(mark(z0))), MARK(recip(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(0) -> c(A__SQR(0), MARK(0)) A__TERMS(nil) -> c(A__SQR(nil), MARK(nil)) S tuples: A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(cons(z0, z1)) -> c(A__SQR(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(A__SQR(recip(mark(z0))), MARK(recip(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(0) -> c(A__SQR(0), MARK(0)) A__TERMS(nil) -> c(A__SQR(nil), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__SQR_1, A__DBL_1, A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1 Compound Symbols: c3_3, c4_3, c7_2, c9_1, c10_2, c11_2, c14_1, c18_2, c19_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2 ---------------------------------------- (71) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__TERMS(0) -> c(A__SQR(0), MARK(0)) A__TERMS(nil) -> c(A__SQR(nil), MARK(nil)) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(cons(z0, z1)) -> c(A__SQR(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(A__SQR(recip(mark(z0))), MARK(recip(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) S tuples: A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(cons(z0, z1)) -> c(A__SQR(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(A__SQR(recip(mark(z0))), MARK(recip(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__SQR_1, A__DBL_1, A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1 Compound Symbols: c3_3, c4_3, c7_2, c9_1, c10_2, c11_2, c14_1, c18_2, c19_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) S tuples: A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__SQR_1, A__DBL_1, A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1 Compound Symbols: c3_3, c4_3, c7_2, c9_1, c10_2, c11_2, c14_1, c18_2, c19_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(z0)) -> c3(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__SQR(mark(z0)), MARK(z0)) by A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0)), MARK(0)) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil)), MARK(nil)) A__SQR(s(x0)) -> c3(A__ADD(sqr(mark(x0)), a__dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0)), MARK(0)) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil)), 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0)), MARK(0)) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil)), MARK(nil)) A__SQR(s(x0)) -> c3(A__ADD(sqr(mark(x0)), a__dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0)), MARK(0)) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil)), MARK(nil)) S tuples: A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0)), MARK(0)) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil)), MARK(nil)) A__SQR(s(x0)) -> c3(A__ADD(sqr(mark(x0)), a__dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0)), MARK(0)) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil)), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__SQR_1, A__DBL_1, A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1 Compound Symbols: c4_3, c7_2, c9_1, c10_2, c11_2, c14_1, c18_2, c19_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3 ---------------------------------------- (77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) S tuples: A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__SQR_1, A__DBL_1, A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1 Compound Symbols: c4_3, c7_2, c9_1, c10_2, c11_2, c14_1, c18_2, c19_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(z0)) -> c4(A__ADD(a__sqr(mark(z0)), a__dbl(mark(z0))), A__DBL(mark(z0)), MARK(z0)) by A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0)), MARK(0)) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil)), MARK(nil)) A__SQR(s(x0)) -> c4(A__ADD(sqr(mark(x0)), a__dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0)), MARK(0)) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil)), MARK(nil)) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0)), MARK(0)) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil)), MARK(nil)) A__SQR(s(x0)) -> c4(A__ADD(sqr(mark(x0)), a__dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0)), MARK(0)) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil)), MARK(nil)) S tuples: A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0)), MARK(0)) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil)), MARK(nil)) A__SQR(s(x0)) -> c4(A__ADD(sqr(mark(x0)), a__dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0)), MARK(0)) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil)), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__DBL_1, A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1 Compound Symbols: c7_2, c9_1, c10_2, c11_2, c14_1, c18_2, c19_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3 ---------------------------------------- (81) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) S tuples: A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__DBL_1, A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1 Compound Symbols: c7_2, c9_1, c10_2, c11_2, c14_1, c18_2, c19_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2 ---------------------------------------- (83) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__DBL(s(z0)) -> c7(A__DBL(mark(z0)), MARK(z0)) by A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(cons(z0, z1))) -> c7(A__DBL(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(A__DBL(recip(mark(z0))), MARK(recip(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(0)) -> c7(A__DBL(0), MARK(0)) A__DBL(s(nil)) -> c7(A__DBL(nil), MARK(nil)) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(cons(z0, z1))) -> c7(A__DBL(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(A__DBL(recip(mark(z0))), MARK(recip(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(0)) -> c7(A__DBL(0), MARK(0)) A__DBL(s(nil)) -> c7(A__DBL(nil), MARK(nil)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(cons(z0, z1))) -> c7(A__DBL(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(A__DBL(recip(mark(z0))), MARK(recip(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(0)) -> c7(A__DBL(0), MARK(0)) A__DBL(s(nil)) -> c7(A__DBL(nil), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c10_2, c11_2, c14_1, c18_2, c19_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2 ---------------------------------------- (85) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__DBL(s(nil)) -> c7(A__DBL(nil), MARK(nil)) A__DBL(s(0)) -> c7(A__DBL(0), MARK(0)) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(cons(z0, z1))) -> c7(A__DBL(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(A__DBL(recip(mark(z0))), MARK(recip(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(cons(z0, z1))) -> c7(A__DBL(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(A__DBL(recip(mark(z0))), MARK(recip(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c10_2, c11_2, c14_1, c18_2, c19_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2 ---------------------------------------- (87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c10_2, c11_2, c14_1, c18_2, c19_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(z0), z1) -> c10(A__ADD(mark(z0), mark(z1)), MARK(z0)) by A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1)), MARK(0)) A__ADD(s(nil), x1) -> c10(A__ADD(nil, mark(x1)), MARK(nil)) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1)), MARK(0)) A__ADD(s(nil), x1) -> c10(A__ADD(nil, mark(x1)), MARK(nil)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1)), MARK(0)) A__ADD(s(nil), x1) -> c10(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, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c11_2, c14_1, c18_2, c19_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2 ---------------------------------------- (91) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__ADD(s(nil), x1) -> c10(A__ADD(nil, 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1)), MARK(0)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c10(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, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c11_2, c14_1, c18_2, c19_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2 ---------------------------------------- (93) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(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, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c11_2, c14_1, c18_2, c19_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1 ---------------------------------------- (95) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(z0), z1) -> c11(A__ADD(mark(z0), mark(z1)), MARK(z1)) by A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0), MARK(0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil), MARK(nil)) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(cons(z0, z1)), x1) -> c11(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(A__ADD(recip(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(nil), x1) -> c11(A__ADD(nil, mark(x1)), MARK(x1)) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0), MARK(0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil), MARK(nil)) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(cons(z0, z1)), x1) -> c11(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(A__ADD(recip(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(nil), x1) -> c11(A__ADD(nil, mark(x1)), MARK(x1)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0), MARK(0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil), MARK(nil)) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(cons(z0, z1)), x1) -> c11(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(A__ADD(recip(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(nil), x1) -> c11(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, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c18_2, c19_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2 ---------------------------------------- (97) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c18_2, c19_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (99) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__HALF(s(s(z0))) -> c18(A__HALF(mark(z0)), MARK(z0)) by A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(A__HALF(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(A__HALF(recip(mark(z0))), MARK(recip(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(0))) -> c18(A__HALF(0), MARK(0)) A__HALF(s(s(nil))) -> c18(A__HALF(nil), MARK(nil)) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(A__HALF(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(A__HALF(recip(mark(z0))), MARK(recip(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(0))) -> c18(A__HALF(0), MARK(0)) A__HALF(s(s(nil))) -> c18(A__HALF(nil), MARK(nil)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(A__HALF(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(A__HALF(recip(mark(z0))), MARK(recip(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(0))) -> c18(A__HALF(0), MARK(0)) A__HALF(s(s(nil))) -> c18(A__HALF(nil), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2 ---------------------------------------- (101) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__HALF(s(s(nil))) -> c18(A__HALF(nil), MARK(nil)) A__HALF(s(s(0))) -> c18(A__HALF(0), MARK(0)) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(A__HALF(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(A__HALF(recip(mark(z0))), MARK(recip(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(A__HALF(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(A__HALF(recip(mark(z0))), MARK(recip(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2 ---------------------------------------- (103) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(terms(z0)) -> c21(A__TERMS(mark(z0)), MARK(z0)) by MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(terms(0)) -> c21(A__TERMS(0), MARK(0)) MARK(terms(nil)) -> c21(A__TERMS(nil), MARK(nil)) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(terms(0)) -> c21(A__TERMS(0), MARK(0)) MARK(terms(nil)) -> c21(A__TERMS(nil), MARK(nil)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(terms(0)) -> c21(A__TERMS(0), MARK(0)) MARK(terms(nil)) -> c21(A__TERMS(nil), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2 ---------------------------------------- (107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(terms(nil)) -> c21(A__TERMS(nil), MARK(nil)) MARK(terms(0)) -> c21(A__TERMS(0), MARK(0)) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sqr(z0)) -> c22(A__SQR(mark(z0)), MARK(z0)) by MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(cons(z0, z1))) -> c22(A__SQR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(A__SQR(recip(mark(z0))), MARK(recip(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(0)) -> c22(A__SQR(0), MARK(0)) MARK(sqr(nil)) -> c22(A__SQR(nil), 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(cons(z0, z1))) -> c22(A__SQR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(A__SQR(recip(mark(z0))), MARK(recip(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(0)) -> c22(A__SQR(0), MARK(0)) MARK(sqr(nil)) -> c22(A__SQR(nil), MARK(nil)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(cons(z0, z1))) -> c22(A__SQR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(A__SQR(recip(mark(z0))), MARK(recip(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(0)) -> c22(A__SQR(0), MARK(0)) MARK(sqr(nil)) -> c22(A__SQR(nil), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2 ---------------------------------------- (111) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(sqr(nil)) -> c22(A__SQR(nil), MARK(nil)) MARK(sqr(0)) -> c22(A__SQR(0), MARK(0)) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(cons(z0, z1))) -> c22(A__SQR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(A__SQR(recip(mark(z0))), MARK(recip(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(cons(z0, z1))) -> c22(A__SQR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(A__SQR(recip(mark(z0))), MARK(recip(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2 ---------------------------------------- (113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1 ---------------------------------------- (115) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(z0, z1)) -> c23(A__ADD(mark(z0), mark(z1)), MARK(z0)) by MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(cons(z0, z1), x1)) -> c23(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1)), MARK(0)) MARK(add(nil, x1)) -> c23(A__ADD(nil, mark(x1)), 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(cons(z0, z1), x1)) -> c23(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1)), MARK(0)) MARK(add(nil, x1)) -> c23(A__ADD(nil, mark(x1)), MARK(nil)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(cons(z0, z1), x1)) -> c23(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1)), MARK(0)) MARK(add(nil, x1)) -> c23(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, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2 ---------------------------------------- (117) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(add(nil, x1)) -> c23(A__ADD(nil, mark(x1)), 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(cons(z0, z1), x1)) -> c23(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1)), MARK(0)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(cons(z0, z1), x1)) -> c23(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c23(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, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2 ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(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, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c24_2, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(z0, z1)) -> c24(A__ADD(mark(z0), mark(z1)), MARK(z1)) by MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0), MARK(0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil), MARK(nil)) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c24(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(add(recip(z0), x1)) -> c24(A__ADD(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(nil, x1)) -> c24(A__ADD(nil, mark(x1)), MARK(x1)) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0), MARK(0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil), MARK(nil)) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c24(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(add(recip(z0), x1)) -> c24(A__ADD(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(nil, x1)) -> c24(A__ADD(nil, mark(x1)), MARK(x1)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0), MARK(0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil), MARK(nil)) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c24(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(add(recip(z0), x1)) -> c24(A__ADD(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(nil, x1)) -> c24(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, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2 ---------------------------------------- (123) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c25_2, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1 ---------------------------------------- (125) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(dbl(z0)) -> c25(A__DBL(mark(z0)), MARK(z0)) by MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(cons(z0, z1))) -> c25(A__DBL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(A__DBL(recip(mark(z0))), MARK(recip(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(0)) -> c25(A__DBL(0), MARK(0)) MARK(dbl(nil)) -> c25(A__DBL(nil), MARK(nil)) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(cons(z0, z1))) -> c25(A__DBL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(A__DBL(recip(mark(z0))), MARK(recip(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(0)) -> c25(A__DBL(0), MARK(0)) MARK(dbl(nil)) -> c25(A__DBL(nil), MARK(nil)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(cons(z0, z1))) -> c25(A__DBL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(A__DBL(recip(mark(z0))), MARK(recip(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(0)) -> c25(A__DBL(0), MARK(0)) MARK(dbl(nil)) -> c25(A__DBL(nil), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2 ---------------------------------------- (127) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(dbl(0)) -> c25(A__DBL(0), MARK(0)) MARK(dbl(nil)) -> c25(A__DBL(nil), 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(cons(z0, z1))) -> c25(A__DBL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(A__DBL(recip(mark(z0))), MARK(recip(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(cons(z0, z1))) -> c25(A__DBL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(A__DBL(recip(mark(z0))), MARK(recip(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2 ---------------------------------------- (129) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c26_2, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1 ---------------------------------------- (131) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(z0, z1)) -> c26(A__FIRST(mark(z0), mark(z1)), MARK(z0)) by MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(x0, recip(z0))) -> c26(A__FIRST(mark(x0), recip(mark(z0))), MARK(x0)) MARK(first(x0, s(z0))) -> c26(A__FIRST(mark(x0), s(mark(z0))), MARK(x0)) MARK(first(x0, 0)) -> c26(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c26(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(cons(z0, z1), x1)) -> c26(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(A__FIRST(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(0, x1)) -> c26(A__FIRST(0, mark(x1)), MARK(0)) MARK(first(nil, x1)) -> c26(A__FIRST(nil, mark(x1)), MARK(nil)) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(x0, recip(z0))) -> c26(A__FIRST(mark(x0), recip(mark(z0))), MARK(x0)) MARK(first(x0, s(z0))) -> c26(A__FIRST(mark(x0), s(mark(z0))), MARK(x0)) MARK(first(x0, 0)) -> c26(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c26(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(cons(z0, z1), x1)) -> c26(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(A__FIRST(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(0, x1)) -> c26(A__FIRST(0, mark(x1)), MARK(0)) MARK(first(nil, x1)) -> c26(A__FIRST(nil, mark(x1)), MARK(nil)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(x0, recip(z0))) -> c26(A__FIRST(mark(x0), recip(mark(z0))), MARK(x0)) MARK(first(x0, s(z0))) -> c26(A__FIRST(mark(x0), s(mark(z0))), MARK(x0)) MARK(first(x0, 0)) -> c26(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c26(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(cons(z0, z1), x1)) -> c26(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(A__FIRST(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(0, x1)) -> c26(A__FIRST(0, mark(x1)), MARK(0)) MARK(first(nil, x1)) -> c26(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, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2 ---------------------------------------- (133) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(0, x1)) -> c26(A__FIRST(0, mark(x1)), MARK(0)) MARK(first(nil, x1)) -> c26(A__FIRST(nil, mark(x1)), 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(x0, recip(z0))) -> c26(A__FIRST(mark(x0), recip(mark(z0))), MARK(x0)) MARK(first(x0, s(z0))) -> c26(A__FIRST(mark(x0), s(mark(z0))), MARK(x0)) MARK(first(x0, 0)) -> c26(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c26(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(cons(z0, z1), x1)) -> c26(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(A__FIRST(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(x0, recip(z0))) -> c26(A__FIRST(mark(x0), recip(mark(z0))), MARK(x0)) MARK(first(x0, s(z0))) -> c26(A__FIRST(mark(x0), s(mark(z0))), MARK(x0)) MARK(first(x0, 0)) -> c26(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c26(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(cons(z0, z1), x1)) -> c26(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(A__FIRST(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(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, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2 ---------------------------------------- (135) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c27_2, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (137) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(z0, z1)) -> c27(A__FIRST(mark(z0), mark(z1)), MARK(z1)) by MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(x0, recip(z0))) -> c27(A__FIRST(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(A__FIRST(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(first(x0, 0)) -> c27(A__FIRST(mark(x0), 0), MARK(0)) MARK(first(x0, nil)) -> c27(A__FIRST(mark(x0), nil), MARK(nil)) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c27(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(first(recip(z0), x1)) -> c27(A__FIRST(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c27(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c27(A__FIRST(nil, mark(x1)), MARK(x1)) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(x0, recip(z0))) -> c27(A__FIRST(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(A__FIRST(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(first(x0, 0)) -> c27(A__FIRST(mark(x0), 0), MARK(0)) MARK(first(x0, nil)) -> c27(A__FIRST(mark(x0), nil), MARK(nil)) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c27(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(first(recip(z0), x1)) -> c27(A__FIRST(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c27(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c27(A__FIRST(nil, mark(x1)), MARK(x1)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(x0, recip(z0))) -> c27(A__FIRST(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(A__FIRST(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(first(x0, 0)) -> c27(A__FIRST(mark(x0), 0), MARK(0)) MARK(first(x0, nil)) -> c27(A__FIRST(mark(x0), nil), MARK(nil)) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c27(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(first(recip(z0), x1)) -> c27(A__FIRST(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c27(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c27(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, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2 ---------------------------------------- (139) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(x0, 0)) -> c27(A__FIRST(mark(x0), 0), MARK(0)) MARK(first(x0, nil)) -> c27(A__FIRST(mark(x0), 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(x0, recip(z0))) -> c27(A__FIRST(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(A__FIRST(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c27(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(first(recip(z0), x1)) -> c27(A__FIRST(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c27(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c27(A__FIRST(nil, mark(x1)), MARK(x1)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(x0, recip(z0))) -> c27(A__FIRST(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(A__FIRST(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c27(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(first(recip(z0), x1)) -> c27(A__FIRST(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c27(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c27(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, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2 ---------------------------------------- (141) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c28_2, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1 ---------------------------------------- (143) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(half(z0)) -> c28(A__HALF(mark(z0)), MARK(z0)) by MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(cons(z0, z1))) -> c28(A__HALF(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(A__HALF(recip(mark(z0))), MARK(recip(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(0)) -> c28(A__HALF(0), MARK(0)) MARK(half(nil)) -> c28(A__HALF(nil), MARK(nil)) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(cons(z0, z1))) -> c28(A__HALF(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(A__HALF(recip(mark(z0))), MARK(recip(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(0)) -> c28(A__HALF(0), MARK(0)) MARK(half(nil)) -> c28(A__HALF(nil), MARK(nil)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(cons(z0, z1))) -> c28(A__HALF(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(A__HALF(recip(mark(z0))), MARK(recip(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(0)) -> c28(A__HALF(0), MARK(0)) MARK(half(nil)) -> c28(A__HALF(nil), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2 ---------------------------------------- (145) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(half(0)) -> c28(A__HALF(0), MARK(0)) MARK(half(nil)) -> c28(A__HALF(nil), MARK(nil)) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(cons(z0, z1))) -> c28(A__HALF(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(A__HALF(recip(mark(z0))), MARK(recip(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(cons(z0, z1))) -> c28(A__HALF(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(A__HALF(recip(mark(z0))), MARK(recip(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2 ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (149) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__TERMS(terms(z0)) -> c(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) by A__TERMS(terms(x0)) -> c(A__SQR(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), MARK(terms(x0))) A__TERMS(terms(x0)) -> c(A__SQR(terms(mark(x0))), MARK(terms(x0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0)), MARK(terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil)), MARK(terms(nil))) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(x0)) -> c(A__SQR(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), MARK(terms(x0))) A__TERMS(terms(x0)) -> c(A__SQR(terms(mark(x0))), MARK(terms(x0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0)), MARK(terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil)), MARK(terms(nil))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(x0)) -> c(A__SQR(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), MARK(terms(x0))) A__TERMS(terms(x0)) -> c(A__SQR(terms(mark(x0))), MARK(terms(x0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0)), MARK(terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil)), MARK(terms(nil))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (151) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (153) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__TERMS(sqr(z0)) -> c(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) by A__TERMS(sqr(x0)) -> c(A__SQR(sqr(mark(x0))), MARK(sqr(x0))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0)), MARK(sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil)), MARK(sqr(nil))) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(x0)) -> c(A__SQR(sqr(mark(x0))), MARK(sqr(x0))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0)), MARK(sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil)), MARK(sqr(nil))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(x0)) -> c(A__SQR(sqr(mark(x0))), MARK(sqr(x0))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0)), MARK(sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil)), MARK(sqr(nil))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (155) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (157) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__TERMS(add(z0, z1)) -> c(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) by A__TERMS(add(x0, x1)) -> c(A__SQR(add(mark(x0), mark(x1))), MARK(add(x0, x1))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, x1)) -> c(A__SQR(add(mark(x0), mark(x1))), MARK(add(x0, x1))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, x1)) -> c(A__SQR(add(mark(x0), mark(x1))), MARK(add(x0, x1))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), 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, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(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, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (161) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__TERMS(dbl(z0)) -> c(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) by A__TERMS(dbl(x0)) -> c(A__SQR(dbl(mark(x0))), MARK(dbl(x0))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0)), MARK(dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil)), MARK(dbl(nil))) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) 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z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(x0)) -> c(A__SQR(dbl(mark(x0))), MARK(dbl(x0))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0)), MARK(dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil)), MARK(dbl(nil))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(x0)) -> c(A__SQR(dbl(mark(x0))), MARK(dbl(x0))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0)), MARK(dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil)), MARK(dbl(nil))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (163) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) 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z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (165) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) by A__TERMS(first(x0, x1)) -> c(A__SQR(first(mark(x0), mark(x1))), MARK(first(x0, x1))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, x1)) -> c(A__SQR(first(mark(x0), mark(x1))), MARK(first(x0, x1))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, x1)) -> c(A__SQR(first(mark(x0), mark(x1))), MARK(first(x0, x1))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), 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, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (167) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> 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MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(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, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (169) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__TERMS(half(z0)) -> c(A__SQR(a__half(mark(z0))), MARK(half(z0))) by A__TERMS(half(x0)) -> c(A__SQR(half(mark(x0))), MARK(half(x0))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(0)) -> c(A__SQR(a__half(0)), MARK(half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil)), MARK(half(nil))) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(x0)) -> c(A__SQR(half(mark(x0))), MARK(half(x0))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(0)) -> c(A__SQR(a__half(0)), MARK(half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil)), MARK(half(nil))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(x0)) -> c(A__SQR(half(mark(x0))), MARK(half(x0))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(0)) -> c(A__SQR(a__half(0)), MARK(half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil)), MARK(half(nil))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (171) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (173) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(x0)) -> c3(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) by A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0)), MARK(0)) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil)), MARK(nil)) A__SQR(s(x0)) -> c3(A__ADD(sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0)), MARK(0)) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil)), MARK(nil)) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> 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z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0)), MARK(0)) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil)), MARK(nil)) A__SQR(s(x0)) -> c3(A__ADD(sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0)), MARK(0)) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil)), MARK(nil)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> 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z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0)), MARK(0)) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil)), MARK(nil)) A__SQR(s(x0)) -> c3(A__ADD(sqr(mark(x0)), dbl(mark(x0))), A__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0)), MARK(0)) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil)), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (175) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (177) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) by A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), dbl(a__terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0))), MARK(terms(0))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil))), MARK(terms(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(sqr(mark(terms(x0))), a__dbl(a__terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0))), MARK(terms(0))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil))), MARK(terms(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(sqr(mark(terms(x0))), a__dbl(a__terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0))), MARK(terms(0))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil))), MARK(terms(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(sqr(mark(terms(x0))), a__dbl(a__terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (179) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) 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c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) 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c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> 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c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (181) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) by A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), dbl(a__sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0))), MARK(sqr(0))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil))), MARK(sqr(nil))) A__SQR(s(sqr(x0))) -> c3(A__ADD(sqr(mark(sqr(x0))), a__dbl(a__sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0))), MARK(sqr(0))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil))), MARK(sqr(nil))) A__SQR(s(sqr(x0))) -> c3(A__ADD(sqr(mark(sqr(x0))), a__dbl(a__sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0))), MARK(sqr(0))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil))), MARK(sqr(nil))) A__SQR(s(sqr(x0))) -> c3(A__ADD(sqr(mark(sqr(x0))), a__dbl(a__sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (183) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) 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A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (185) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) by A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), dbl(a__add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(sqr(mark(add(x0, x1))), a__dbl(a__add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(sqr(mark(add(x0, x1))), a__dbl(a__add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(sqr(mark(add(x0, x1))), a__dbl(a__add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (187) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> 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c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), 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, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (189) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) by A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), dbl(a__dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0))), MARK(dbl(0))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil))), MARK(dbl(nil))) A__SQR(s(dbl(x0))) -> c3(A__ADD(sqr(mark(dbl(x0))), a__dbl(a__dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0))), MARK(dbl(0))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil))), MARK(dbl(nil))) A__SQR(s(dbl(x0))) -> c3(A__ADD(sqr(mark(dbl(x0))), a__dbl(a__dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> 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c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0))), MARK(dbl(0))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil))), MARK(dbl(nil))) A__SQR(s(dbl(x0))) -> c3(A__ADD(sqr(mark(dbl(x0))), a__dbl(a__dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (191) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (193) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) by A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), dbl(a__first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(sqr(mark(first(x0, x1))), a__dbl(a__first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), 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c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> 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x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, 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c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(sqr(mark(first(x0, x1))), a__dbl(a__first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), 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A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> 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c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(sqr(mark(first(x0, x1))), a__dbl(a__first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (195) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), 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, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (197) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) by A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), dbl(a__half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0))), MARK(half(0))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil))), MARK(half(nil))) A__SQR(s(half(x0))) -> c3(A__ADD(sqr(mark(half(x0))), a__dbl(a__half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0))), MARK(half(0))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil))), MARK(half(nil))) A__SQR(s(half(x0))) -> c3(A__ADD(sqr(mark(half(x0))), a__dbl(a__half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0))), MARK(half(0))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil))), MARK(half(nil))) A__SQR(s(half(x0))) -> c3(A__ADD(sqr(mark(half(x0))), a__dbl(a__half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (199) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (201) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) by A__SQR(s(cons(x0, x1))) -> c3(A__ADD(a__sqr(mark(cons(x0, x1))), dbl(cons(mark(x0), x1))), A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(x0, x1))) -> c3(A__ADD(sqr(mark(cons(x0, x1))), a__dbl(cons(mark(x0), x1))), A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(x0, x1))) -> c3(A__ADD(sqr(mark(cons(x0, x1))), a__dbl(cons(mark(x0), x1))), A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(x0, x1))) -> c3(A__ADD(sqr(mark(cons(x0, x1))), a__dbl(cons(mark(x0), x1))), A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (203) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (205) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) by A__SQR(s(recip(x0))) -> c3(A__ADD(a__sqr(mark(recip(x0))), dbl(recip(mark(x0)))), A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(x0))) -> c3(A__ADD(sqr(mark(recip(x0))), a__dbl(recip(mark(x0)))), A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(x0))) -> c3(A__ADD(sqr(mark(recip(x0))), a__dbl(recip(mark(x0)))), A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> 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mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(x0))) -> c3(A__ADD(sqr(mark(recip(x0))), a__dbl(recip(mark(x0)))), A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (207) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (209) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) by A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), dbl(s(mark(x0)))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(x0))) -> c3(A__ADD(sqr(mark(s(x0))), a__dbl(s(mark(x0)))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(x0))) -> c3(A__ADD(sqr(mark(s(x0))), a__dbl(s(mark(x0)))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), 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MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), 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A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(x0))) -> c3(A__ADD(sqr(mark(s(x0))), a__dbl(s(mark(x0)))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (211) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (213) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) by A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(a__terms(mark(x0))), dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(x0))) -> c3(A__ADD(sqr(a__terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0))), MARK(terms(0))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil))), MARK(terms(nil))) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(sqr(a__terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0))), MARK(terms(0))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil))), MARK(terms(nil))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(sqr(a__terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0))), MARK(terms(0))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil))), MARK(terms(nil))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (215) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> 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z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (217) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) by A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(a__sqr(mark(x0))), dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(sqr(a__sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0))), MARK(sqr(0))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil))), MARK(sqr(nil))) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(sqr(a__sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0))), MARK(sqr(0))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil))), MARK(sqr(nil))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(sqr(a__sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0))), MARK(sqr(0))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil))), MARK(sqr(nil))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (219) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> 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s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (221) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) by A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(a__add(mark(x0), mark(x1))), dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(sqr(a__add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(sqr(a__add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, 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A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> 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MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, 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c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(sqr(a__add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), 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, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (223) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), 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, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (225) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) by A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(a__dbl(mark(x0))), dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(x0))) -> c3(A__ADD(sqr(a__dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__terms(mark(z0)))), a__dbl(mark(dbl(terms(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__sqr(mark(z0)))), a__dbl(mark(dbl(sqr(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__add(mark(z0), mark(z1)))), a__dbl(mark(dbl(add(z0, z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__dbl(mark(z0)))), a__dbl(mark(dbl(dbl(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__first(mark(z0), mark(z1)))), a__dbl(mark(dbl(first(z0, z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__half(mark(z0)))), a__dbl(mark(dbl(half(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(cons(mark(z0), z1))), a__dbl(mark(dbl(cons(z0, z1))))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(a__dbl(recip(mark(z0)))), a__dbl(mark(dbl(recip(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(a__dbl(s(mark(z0)))), a__dbl(mark(dbl(s(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(a__dbl(0)), a__dbl(mark(dbl(0)))), A__SQR(mark(dbl(0))), MARK(dbl(0))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(a__dbl(nil)), a__dbl(mark(dbl(nil)))), A__SQR(mark(dbl(nil))), MARK(dbl(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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(sqr(a__dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__terms(mark(z0)))), a__dbl(mark(dbl(terms(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__sqr(mark(z0)))), a__dbl(mark(dbl(sqr(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__add(mark(z0), mark(z1)))), a__dbl(mark(dbl(add(z0, z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__dbl(mark(z0)))), a__dbl(mark(dbl(dbl(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__first(mark(z0), mark(z1)))), a__dbl(mark(dbl(first(z0, z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__half(mark(z0)))), a__dbl(mark(dbl(half(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(cons(mark(z0), z1))), a__dbl(mark(dbl(cons(z0, z1))))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(a__dbl(recip(mark(z0)))), a__dbl(mark(dbl(recip(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(a__dbl(s(mark(z0)))), a__dbl(mark(dbl(s(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(a__dbl(0)), a__dbl(mark(dbl(0)))), A__SQR(mark(dbl(0))), MARK(dbl(0))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(a__dbl(nil)), a__dbl(mark(dbl(nil)))), A__SQR(mark(dbl(nil))), MARK(dbl(nil))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(sqr(a__dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__terms(mark(z0)))), a__dbl(mark(dbl(terms(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__sqr(mark(z0)))), a__dbl(mark(dbl(sqr(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__add(mark(z0), mark(z1)))), a__dbl(mark(dbl(add(z0, z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__dbl(mark(z0)))), a__dbl(mark(dbl(dbl(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__first(mark(z0), mark(z1)))), a__dbl(mark(dbl(first(z0, z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__half(mark(z0)))), a__dbl(mark(dbl(half(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(cons(mark(z0), z1))), a__dbl(mark(dbl(cons(z0, z1))))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(a__dbl(recip(mark(z0)))), a__dbl(mark(dbl(recip(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(a__dbl(s(mark(z0)))), a__dbl(mark(dbl(s(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(a__dbl(0)), a__dbl(mark(dbl(0)))), A__SQR(mark(dbl(0))), MARK(dbl(0))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(a__dbl(nil)), a__dbl(mark(dbl(nil)))), A__SQR(mark(dbl(nil))), MARK(dbl(nil))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (227) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__terms(mark(z0)))), a__dbl(mark(dbl(terms(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__sqr(mark(z0)))), a__dbl(mark(dbl(sqr(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__add(mark(z0), mark(z1)))), a__dbl(mark(dbl(add(z0, z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__dbl(mark(z0)))), a__dbl(mark(dbl(dbl(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__first(mark(z0), mark(z1)))), a__dbl(mark(dbl(first(z0, z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__half(mark(z0)))), a__dbl(mark(dbl(half(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(cons(mark(z0), z1))), a__dbl(mark(dbl(cons(z0, z1))))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(a__dbl(recip(mark(z0)))), a__dbl(mark(dbl(recip(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(a__dbl(s(mark(z0)))), a__dbl(mark(dbl(s(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(a__dbl(0)), a__dbl(mark(dbl(0)))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(a__dbl(nil)), a__dbl(mark(dbl(nil)))), A__SQR(mark(dbl(nil)))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__terms(mark(z0)))), a__dbl(mark(dbl(terms(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__sqr(mark(z0)))), a__dbl(mark(dbl(sqr(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__add(mark(z0), mark(z1)))), a__dbl(mark(dbl(add(z0, z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__dbl(mark(z0)))), a__dbl(mark(dbl(dbl(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__first(mark(z0), mark(z1)))), a__dbl(mark(dbl(first(z0, z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__half(mark(z0)))), a__dbl(mark(dbl(half(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(cons(mark(z0), z1))), a__dbl(mark(dbl(cons(z0, z1))))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(a__dbl(recip(mark(z0)))), a__dbl(mark(dbl(recip(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(a__dbl(s(mark(z0)))), a__dbl(mark(dbl(s(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(a__dbl(0)), a__dbl(mark(dbl(0)))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(a__dbl(nil)), a__dbl(mark(dbl(nil)))), A__SQR(mark(dbl(nil)))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (229) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) by A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(a__first(mark(x0), mark(x1))), dbl(mark(first(x0, x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(sqr(a__first(mark(x0), mark(x1))), a__dbl(mark(first(x0, x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(first(mark(x0), mark(x1))), a__dbl(mark(first(x0, x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__terms(mark(z0)))), a__dbl(mark(first(x0, terms(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(first(x0, sqr(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(first(x0, add(z0, z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(first(x0, dbl(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(first(x0, first(z0, z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__half(mark(z0)))), a__dbl(mark(first(x0, half(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), cons(mark(z0), z1))), a__dbl(mark(first(x0, cons(z0, z1))))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), recip(mark(z0)))), a__dbl(mark(first(x0, recip(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), s(mark(z0)))), a__dbl(mark(first(x0, s(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(a__first(mark(x0), 0)), a__dbl(mark(first(x0, 0)))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(a__first(mark(x0), nil)), a__dbl(mark(first(x0, nil)))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__terms(mark(z0)), mark(x1))), a__dbl(mark(first(terms(z0), x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(first(sqr(z0), x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(add(z0, z1), x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(first(dbl(z0), x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(first(z0, z1), x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__half(mark(z0)), mark(x1))), a__dbl(mark(first(half(z0), x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(cons(mark(z0), z1), mark(x1))), a__dbl(mark(first(cons(z0, z1), x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__first(recip(mark(z0)), mark(x1))), a__dbl(mark(first(recip(z0), x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(a__first(s(mark(z0)), mark(x1))), a__dbl(mark(first(s(z0), x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(a__first(0, mark(x1))), a__dbl(mark(first(0, x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(a__first(nil, mark(x1))), a__dbl(mark(first(nil, x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__terms(mark(z0)))), a__dbl(mark(dbl(terms(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__sqr(mark(z0)))), a__dbl(mark(dbl(sqr(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__add(mark(z0), mark(z1)))), a__dbl(mark(dbl(add(z0, z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__dbl(mark(z0)))), a__dbl(mark(dbl(dbl(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__first(mark(z0), mark(z1)))), a__dbl(mark(dbl(first(z0, z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__half(mark(z0)))), a__dbl(mark(dbl(half(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(cons(mark(z0), z1))), a__dbl(mark(dbl(cons(z0, z1))))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(a__dbl(recip(mark(z0)))), a__dbl(mark(dbl(recip(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(a__dbl(s(mark(z0)))), a__dbl(mark(dbl(s(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(a__dbl(0)), a__dbl(mark(dbl(0)))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(a__dbl(nil)), a__dbl(mark(dbl(nil)))), A__SQR(mark(dbl(nil)))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(sqr(a__first(mark(x0), mark(x1))), a__dbl(mark(first(x0, x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(first(mark(x0), mark(x1))), a__dbl(mark(first(x0, x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__terms(mark(z0)))), a__dbl(mark(first(x0, terms(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(first(x0, sqr(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(first(x0, add(z0, z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(first(x0, dbl(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(first(x0, first(z0, z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__half(mark(z0)))), a__dbl(mark(first(x0, half(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), cons(mark(z0), z1))), a__dbl(mark(first(x0, cons(z0, z1))))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), recip(mark(z0)))), a__dbl(mark(first(x0, recip(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), s(mark(z0)))), a__dbl(mark(first(x0, s(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(a__first(mark(x0), 0)), a__dbl(mark(first(x0, 0)))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(a__first(mark(x0), nil)), a__dbl(mark(first(x0, nil)))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__terms(mark(z0)), mark(x1))), a__dbl(mark(first(terms(z0), x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(first(sqr(z0), x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(add(z0, z1), x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(first(dbl(z0), x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(first(z0, z1), x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__half(mark(z0)), mark(x1))), a__dbl(mark(first(half(z0), x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(cons(mark(z0), z1), mark(x1))), a__dbl(mark(first(cons(z0, z1), x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__first(recip(mark(z0)), mark(x1))), a__dbl(mark(first(recip(z0), x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(a__first(s(mark(z0)), mark(x1))), a__dbl(mark(first(s(z0), x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(a__first(0, mark(x1))), a__dbl(mark(first(0, x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(a__first(nil, mark(x1))), a__dbl(mark(first(nil, x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, 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c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__terms(mark(z0)))), a__dbl(mark(dbl(terms(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__sqr(mark(z0)))), a__dbl(mark(dbl(sqr(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__add(mark(z0), mark(z1)))), a__dbl(mark(dbl(add(z0, z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__dbl(mark(z0)))), a__dbl(mark(dbl(dbl(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__first(mark(z0), mark(z1)))), a__dbl(mark(dbl(first(z0, z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__half(mark(z0)))), a__dbl(mark(dbl(half(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(cons(mark(z0), z1))), a__dbl(mark(dbl(cons(z0, z1))))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(a__dbl(recip(mark(z0)))), a__dbl(mark(dbl(recip(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(a__dbl(s(mark(z0)))), a__dbl(mark(dbl(s(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(a__dbl(0)), a__dbl(mark(dbl(0)))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(a__dbl(nil)), a__dbl(mark(dbl(nil)))), A__SQR(mark(dbl(nil)))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(sqr(a__first(mark(x0), mark(x1))), a__dbl(mark(first(x0, x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(first(mark(x0), mark(x1))), a__dbl(mark(first(x0, x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__terms(mark(z0)))), a__dbl(mark(first(x0, terms(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(first(x0, sqr(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(first(x0, add(z0, z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(first(x0, dbl(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(first(x0, first(z0, z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__half(mark(z0)))), a__dbl(mark(first(x0, half(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), cons(mark(z0), z1))), a__dbl(mark(first(x0, cons(z0, z1))))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), recip(mark(z0)))), a__dbl(mark(first(x0, recip(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), s(mark(z0)))), a__dbl(mark(first(x0, s(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(a__first(mark(x0), 0)), a__dbl(mark(first(x0, 0)))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(a__first(mark(x0), nil)), a__dbl(mark(first(x0, nil)))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__terms(mark(z0)), mark(x1))), a__dbl(mark(first(terms(z0), x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(first(sqr(z0), x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(add(z0, z1), x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(first(dbl(z0), x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(first(z0, z1), x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__half(mark(z0)), mark(x1))), a__dbl(mark(first(half(z0), x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(cons(mark(z0), z1), mark(x1))), a__dbl(mark(first(cons(z0, z1), x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__first(recip(mark(z0)), mark(x1))), a__dbl(mark(first(recip(z0), x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(a__first(s(mark(z0)), mark(x1))), a__dbl(mark(first(s(z0), x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(a__first(0, mark(x1))), a__dbl(mark(first(0, x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(a__first(nil, mark(x1))), a__dbl(mark(first(nil, x1)))), A__SQR(mark(first(nil, x1))), 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, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (231) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> 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c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) 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s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__terms(mark(z0)))), a__dbl(mark(dbl(terms(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__sqr(mark(z0)))), a__dbl(mark(dbl(sqr(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__add(mark(z0), mark(z1)))), a__dbl(mark(dbl(add(z0, z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__dbl(mark(z0)))), a__dbl(mark(dbl(dbl(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__first(mark(z0), mark(z1)))), a__dbl(mark(dbl(first(z0, z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__half(mark(z0)))), a__dbl(mark(dbl(half(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(cons(mark(z0), z1))), a__dbl(mark(dbl(cons(z0, z1))))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(a__dbl(recip(mark(z0)))), a__dbl(mark(dbl(recip(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(a__dbl(s(mark(z0)))), a__dbl(mark(dbl(s(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(a__dbl(0)), a__dbl(mark(dbl(0)))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(a__dbl(nil)), a__dbl(mark(dbl(nil)))), A__SQR(mark(dbl(nil)))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(first(mark(x0), mark(x1))), a__dbl(mark(first(x0, x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__terms(mark(z0)))), a__dbl(mark(first(x0, terms(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(first(x0, sqr(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(first(x0, add(z0, z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(first(x0, dbl(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(first(x0, first(z0, z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__half(mark(z0)))), a__dbl(mark(first(x0, half(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), cons(mark(z0), z1))), a__dbl(mark(first(x0, cons(z0, z1))))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), recip(mark(z0)))), a__dbl(mark(first(x0, recip(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), s(mark(z0)))), a__dbl(mark(first(x0, s(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(a__first(mark(x0), 0)), a__dbl(mark(first(x0, 0)))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(a__first(mark(x0), nil)), a__dbl(mark(first(x0, nil)))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__terms(mark(z0)), mark(x1))), a__dbl(mark(first(terms(z0), x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(first(sqr(z0), x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(add(z0, z1), x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(first(dbl(z0), x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(first(z0, z1), x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__half(mark(z0)), mark(x1))), a__dbl(mark(first(half(z0), x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(cons(mark(z0), z1), mark(x1))), a__dbl(mark(first(cons(z0, z1), x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__first(recip(mark(z0)), mark(x1))), a__dbl(mark(first(recip(z0), x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(a__first(s(mark(z0)), mark(x1))), a__dbl(mark(first(s(z0), x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(a__first(0, mark(x1))), a__dbl(mark(first(0, x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(a__first(nil, mark(x1))), a__dbl(mark(first(nil, x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__terms(mark(z0)))), a__dbl(mark(dbl(terms(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__sqr(mark(z0)))), a__dbl(mark(dbl(sqr(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__add(mark(z0), mark(z1)))), a__dbl(mark(dbl(add(z0, z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__dbl(mark(z0)))), a__dbl(mark(dbl(dbl(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__first(mark(z0), mark(z1)))), a__dbl(mark(dbl(first(z0, z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__half(mark(z0)))), a__dbl(mark(dbl(half(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(cons(mark(z0), z1))), a__dbl(mark(dbl(cons(z0, z1))))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(a__dbl(recip(mark(z0)))), a__dbl(mark(dbl(recip(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(a__dbl(s(mark(z0)))), a__dbl(mark(dbl(s(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(a__dbl(0)), a__dbl(mark(dbl(0)))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(a__dbl(nil)), a__dbl(mark(dbl(nil)))), A__SQR(mark(dbl(nil)))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(first(mark(x0), mark(x1))), a__dbl(mark(first(x0, x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__terms(mark(z0)))), a__dbl(mark(first(x0, terms(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(first(x0, sqr(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(first(x0, add(z0, z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(first(x0, dbl(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(first(x0, first(z0, z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__half(mark(z0)))), a__dbl(mark(first(x0, half(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), cons(mark(z0), z1))), a__dbl(mark(first(x0, cons(z0, z1))))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), recip(mark(z0)))), a__dbl(mark(first(x0, recip(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), s(mark(z0)))), a__dbl(mark(first(x0, s(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(a__first(mark(x0), 0)), a__dbl(mark(first(x0, 0)))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(a__first(mark(x0), nil)), a__dbl(mark(first(x0, nil)))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__terms(mark(z0)), mark(x1))), a__dbl(mark(first(terms(z0), x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(first(sqr(z0), x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(add(z0, z1), x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(first(dbl(z0), x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(first(z0, z1), x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__half(mark(z0)), mark(x1))), a__dbl(mark(first(half(z0), x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(cons(mark(z0), z1), mark(x1))), a__dbl(mark(first(cons(z0, z1), x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__first(recip(mark(z0)), mark(x1))), a__dbl(mark(first(recip(z0), x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(a__first(s(mark(z0)), mark(x1))), a__dbl(mark(first(s(z0), x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(a__first(0, mark(x1))), a__dbl(mark(first(0, x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(a__first(nil, mark(x1))), a__dbl(mark(first(nil, x1)))), A__SQR(mark(first(nil, x1))), 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, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (233) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) by A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(a__half(mark(x0))), dbl(mark(half(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(x0))) -> c3(A__ADD(sqr(a__half(mark(x0))), a__dbl(mark(half(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(half(mark(x0))), a__dbl(mark(half(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(a__half(a__terms(mark(z0)))), a__dbl(mark(half(terms(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(a__half(a__sqr(mark(z0)))), a__dbl(mark(half(sqr(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__add(mark(z0), mark(z1)))), a__dbl(mark(half(add(z0, z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(a__half(a__dbl(mark(z0)))), a__dbl(mark(half(dbl(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__first(mark(z0), mark(z1)))), a__dbl(mark(half(first(z0, z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(a__half(a__half(mark(z0)))), a__dbl(mark(half(half(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(cons(mark(z0), z1))), a__dbl(mark(half(cons(z0, z1))))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(a__half(recip(mark(z0)))), a__dbl(mark(half(recip(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(a__half(s(mark(z0)))), a__dbl(mark(half(s(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(a__half(0)), a__dbl(mark(half(0)))), A__SQR(mark(half(0))), MARK(half(0))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(a__half(nil)), a__dbl(mark(half(nil)))), A__SQR(mark(half(nil))), MARK(half(nil))) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> 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c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__terms(mark(z0)))), a__dbl(mark(dbl(terms(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__sqr(mark(z0)))), a__dbl(mark(dbl(sqr(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__add(mark(z0), mark(z1)))), a__dbl(mark(dbl(add(z0, z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__dbl(mark(z0)))), a__dbl(mark(dbl(dbl(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__first(mark(z0), mark(z1)))), a__dbl(mark(dbl(first(z0, z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__half(mark(z0)))), a__dbl(mark(dbl(half(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(cons(mark(z0), z1))), a__dbl(mark(dbl(cons(z0, z1))))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(a__dbl(recip(mark(z0)))), a__dbl(mark(dbl(recip(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(a__dbl(s(mark(z0)))), a__dbl(mark(dbl(s(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(a__dbl(0)), a__dbl(mark(dbl(0)))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(a__dbl(nil)), a__dbl(mark(dbl(nil)))), A__SQR(mark(dbl(nil)))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(first(mark(x0), mark(x1))), a__dbl(mark(first(x0, x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__terms(mark(z0)))), a__dbl(mark(first(x0, terms(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(first(x0, sqr(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(first(x0, add(z0, z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(first(x0, dbl(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(first(x0, first(z0, z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__half(mark(z0)))), a__dbl(mark(first(x0, half(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), cons(mark(z0), z1))), a__dbl(mark(first(x0, cons(z0, z1))))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), recip(mark(z0)))), a__dbl(mark(first(x0, recip(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), s(mark(z0)))), a__dbl(mark(first(x0, s(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(a__first(mark(x0), 0)), a__dbl(mark(first(x0, 0)))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(a__first(mark(x0), nil)), a__dbl(mark(first(x0, nil)))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__terms(mark(z0)), mark(x1))), a__dbl(mark(first(terms(z0), x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(first(sqr(z0), x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(add(z0, z1), x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(first(dbl(z0), x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(first(z0, z1), x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__half(mark(z0)), mark(x1))), a__dbl(mark(first(half(z0), x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(cons(mark(z0), z1), mark(x1))), a__dbl(mark(first(cons(z0, z1), x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__first(recip(mark(z0)), mark(x1))), a__dbl(mark(first(recip(z0), x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(a__first(s(mark(z0)), mark(x1))), a__dbl(mark(first(s(z0), x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(a__first(0, mark(x1))), a__dbl(mark(first(0, x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(a__first(nil, mark(x1))), a__dbl(mark(first(nil, x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(sqr(a__half(mark(x0))), a__dbl(mark(half(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(half(mark(x0))), a__dbl(mark(half(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(a__half(a__terms(mark(z0)))), a__dbl(mark(half(terms(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(a__half(a__sqr(mark(z0)))), a__dbl(mark(half(sqr(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__add(mark(z0), mark(z1)))), a__dbl(mark(half(add(z0, z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(a__half(a__dbl(mark(z0)))), a__dbl(mark(half(dbl(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__first(mark(z0), mark(z1)))), a__dbl(mark(half(first(z0, z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(a__half(a__half(mark(z0)))), a__dbl(mark(half(half(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(cons(mark(z0), z1))), a__dbl(mark(half(cons(z0, z1))))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(a__half(recip(mark(z0)))), a__dbl(mark(half(recip(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(a__half(s(mark(z0)))), a__dbl(mark(half(s(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(a__half(0)), a__dbl(mark(half(0)))), A__SQR(mark(half(0))), MARK(half(0))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(a__half(nil)), a__dbl(mark(half(nil)))), A__SQR(mark(half(nil))), MARK(half(nil))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__terms(mark(z0)))), a__dbl(mark(dbl(terms(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__sqr(mark(z0)))), a__dbl(mark(dbl(sqr(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__add(mark(z0), mark(z1)))), a__dbl(mark(dbl(add(z0, z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__dbl(mark(z0)))), a__dbl(mark(dbl(dbl(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__first(mark(z0), mark(z1)))), a__dbl(mark(dbl(first(z0, z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__half(mark(z0)))), a__dbl(mark(dbl(half(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(cons(mark(z0), z1))), a__dbl(mark(dbl(cons(z0, z1))))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(a__dbl(recip(mark(z0)))), a__dbl(mark(dbl(recip(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(a__dbl(s(mark(z0)))), a__dbl(mark(dbl(s(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(a__dbl(0)), a__dbl(mark(dbl(0)))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(a__dbl(nil)), a__dbl(mark(dbl(nil)))), A__SQR(mark(dbl(nil)))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(first(mark(x0), mark(x1))), a__dbl(mark(first(x0, x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__terms(mark(z0)))), a__dbl(mark(first(x0, terms(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(first(x0, sqr(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(first(x0, add(z0, z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(first(x0, dbl(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(first(x0, first(z0, z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__half(mark(z0)))), a__dbl(mark(first(x0, half(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), cons(mark(z0), z1))), a__dbl(mark(first(x0, cons(z0, z1))))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), recip(mark(z0)))), a__dbl(mark(first(x0, recip(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), s(mark(z0)))), a__dbl(mark(first(x0, s(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(a__first(mark(x0), 0)), a__dbl(mark(first(x0, 0)))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(a__first(mark(x0), nil)), a__dbl(mark(first(x0, nil)))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__terms(mark(z0)), mark(x1))), a__dbl(mark(first(terms(z0), x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(first(sqr(z0), x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(add(z0, z1), x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(first(dbl(z0), x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(first(z0, z1), x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__half(mark(z0)), mark(x1))), a__dbl(mark(first(half(z0), x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(cons(mark(z0), z1), mark(x1))), a__dbl(mark(first(cons(z0, z1), x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__first(recip(mark(z0)), mark(x1))), a__dbl(mark(first(recip(z0), x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(a__first(s(mark(z0)), mark(x1))), a__dbl(mark(first(s(z0), x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(a__first(0, mark(x1))), a__dbl(mark(first(0, x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(a__first(nil, mark(x1))), a__dbl(mark(first(nil, x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(sqr(a__half(mark(x0))), a__dbl(mark(half(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(half(mark(x0))), a__dbl(mark(half(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(a__half(a__terms(mark(z0)))), a__dbl(mark(half(terms(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(a__half(a__sqr(mark(z0)))), a__dbl(mark(half(sqr(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__add(mark(z0), mark(z1)))), a__dbl(mark(half(add(z0, z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(a__half(a__dbl(mark(z0)))), a__dbl(mark(half(dbl(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__first(mark(z0), mark(z1)))), a__dbl(mark(half(first(z0, z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(a__half(a__half(mark(z0)))), a__dbl(mark(half(half(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(cons(mark(z0), z1))), a__dbl(mark(half(cons(z0, z1))))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(a__half(recip(mark(z0)))), a__dbl(mark(half(recip(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(a__half(s(mark(z0)))), a__dbl(mark(half(s(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(a__half(0)), a__dbl(mark(half(0)))), A__SQR(mark(half(0))), MARK(half(0))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(a__half(nil)), a__dbl(mark(half(nil)))), A__SQR(mark(half(nil))), MARK(half(nil))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (235) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__terms(mark(z0)))), a__dbl(mark(dbl(terms(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__sqr(mark(z0)))), a__dbl(mark(dbl(sqr(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__add(mark(z0), mark(z1)))), a__dbl(mark(dbl(add(z0, z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__dbl(mark(z0)))), a__dbl(mark(dbl(dbl(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__first(mark(z0), mark(z1)))), a__dbl(mark(dbl(first(z0, z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__half(mark(z0)))), a__dbl(mark(dbl(half(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(cons(mark(z0), z1))), a__dbl(mark(dbl(cons(z0, z1))))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(a__dbl(recip(mark(z0)))), a__dbl(mark(dbl(recip(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(a__dbl(s(mark(z0)))), a__dbl(mark(dbl(s(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(a__dbl(0)), a__dbl(mark(dbl(0)))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(a__dbl(nil)), a__dbl(mark(dbl(nil)))), A__SQR(mark(dbl(nil)))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(first(mark(x0), mark(x1))), a__dbl(mark(first(x0, x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__terms(mark(z0)))), a__dbl(mark(first(x0, terms(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(first(x0, sqr(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(first(x0, add(z0, z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(first(x0, dbl(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(first(x0, first(z0, z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__half(mark(z0)))), a__dbl(mark(first(x0, half(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), cons(mark(z0), z1))), a__dbl(mark(first(x0, cons(z0, z1))))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), recip(mark(z0)))), a__dbl(mark(first(x0, recip(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), s(mark(z0)))), a__dbl(mark(first(x0, s(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(a__first(mark(x0), 0)), a__dbl(mark(first(x0, 0)))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(a__first(mark(x0), nil)), a__dbl(mark(first(x0, nil)))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__terms(mark(z0)), mark(x1))), a__dbl(mark(first(terms(z0), x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(first(sqr(z0), x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(add(z0, z1), x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(first(dbl(z0), x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(first(z0, z1), x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__half(mark(z0)), mark(x1))), a__dbl(mark(first(half(z0), x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(cons(mark(z0), z1), mark(x1))), a__dbl(mark(first(cons(z0, z1), x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__first(recip(mark(z0)), mark(x1))), a__dbl(mark(first(recip(z0), x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(a__first(s(mark(z0)), mark(x1))), a__dbl(mark(first(s(z0), x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(a__first(0, mark(x1))), a__dbl(mark(first(0, x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(a__first(nil, mark(x1))), a__dbl(mark(first(nil, x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(half(mark(x0))), a__dbl(mark(half(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(a__half(a__terms(mark(z0)))), a__dbl(mark(half(terms(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(a__half(a__sqr(mark(z0)))), a__dbl(mark(half(sqr(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__add(mark(z0), mark(z1)))), a__dbl(mark(half(add(z0, z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(a__half(a__dbl(mark(z0)))), a__dbl(mark(half(dbl(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__first(mark(z0), mark(z1)))), a__dbl(mark(half(first(z0, z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(a__half(a__half(mark(z0)))), a__dbl(mark(half(half(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(cons(mark(z0), z1))), a__dbl(mark(half(cons(z0, z1))))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(a__half(recip(mark(z0)))), a__dbl(mark(half(recip(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(a__half(s(mark(z0)))), a__dbl(mark(half(s(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(a__half(0)), a__dbl(mark(half(0)))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(a__half(nil)), a__dbl(mark(half(nil)))), A__SQR(mark(half(nil)))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__terms(mark(z0)))), a__dbl(mark(dbl(terms(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__sqr(mark(z0)))), a__dbl(mark(dbl(sqr(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__add(mark(z0), mark(z1)))), a__dbl(mark(dbl(add(z0, z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__dbl(mark(z0)))), a__dbl(mark(dbl(dbl(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__first(mark(z0), mark(z1)))), a__dbl(mark(dbl(first(z0, z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__half(mark(z0)))), a__dbl(mark(dbl(half(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(cons(mark(z0), z1))), a__dbl(mark(dbl(cons(z0, z1))))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(a__dbl(recip(mark(z0)))), a__dbl(mark(dbl(recip(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(a__dbl(s(mark(z0)))), a__dbl(mark(dbl(s(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(a__dbl(0)), a__dbl(mark(dbl(0)))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(a__dbl(nil)), a__dbl(mark(dbl(nil)))), A__SQR(mark(dbl(nil)))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(first(mark(x0), mark(x1))), a__dbl(mark(first(x0, x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__terms(mark(z0)))), a__dbl(mark(first(x0, terms(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(first(x0, sqr(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(first(x0, add(z0, z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(first(x0, dbl(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(first(x0, first(z0, z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__half(mark(z0)))), a__dbl(mark(first(x0, half(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), cons(mark(z0), z1))), a__dbl(mark(first(x0, cons(z0, z1))))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), recip(mark(z0)))), a__dbl(mark(first(x0, recip(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), s(mark(z0)))), a__dbl(mark(first(x0, s(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(a__first(mark(x0), 0)), a__dbl(mark(first(x0, 0)))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(a__first(mark(x0), nil)), a__dbl(mark(first(x0, nil)))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__terms(mark(z0)), mark(x1))), a__dbl(mark(first(terms(z0), x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(first(sqr(z0), x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(add(z0, z1), x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(first(dbl(z0), x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(first(z0, z1), x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__half(mark(z0)), mark(x1))), a__dbl(mark(first(half(z0), x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(cons(mark(z0), z1), mark(x1))), a__dbl(mark(first(cons(z0, z1), x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__first(recip(mark(z0)), mark(x1))), a__dbl(mark(first(recip(z0), x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(a__first(s(mark(z0)), mark(x1))), a__dbl(mark(first(s(z0), x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(a__first(0, mark(x1))), a__dbl(mark(first(0, x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(a__first(nil, mark(x1))), a__dbl(mark(first(nil, x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(half(mark(x0))), a__dbl(mark(half(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(a__half(a__terms(mark(z0)))), a__dbl(mark(half(terms(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(a__half(a__sqr(mark(z0)))), a__dbl(mark(half(sqr(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__add(mark(z0), mark(z1)))), a__dbl(mark(half(add(z0, z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(a__half(a__dbl(mark(z0)))), a__dbl(mark(half(dbl(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__first(mark(z0), mark(z1)))), a__dbl(mark(half(first(z0, z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(a__half(a__half(mark(z0)))), a__dbl(mark(half(half(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(cons(mark(z0), z1))), a__dbl(mark(half(cons(z0, z1))))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(a__half(recip(mark(z0)))), a__dbl(mark(half(recip(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(a__half(s(mark(z0)))), a__dbl(mark(half(s(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(a__half(0)), a__dbl(mark(half(0)))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(a__half(nil)), a__dbl(mark(half(nil)))), A__SQR(mark(half(nil)))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (237) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) by A__SQR(s(cons(x0, x1))) -> c3(A__ADD(a__sqr(cons(mark(x0), x1)), dbl(mark(cons(x0, x1)))), A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__ADD(sqr(cons(mark(x0), x1)), a__dbl(mark(cons(x0, x1)))), A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__terms(mark(z0)), x1)), a__dbl(mark(cons(terms(z0), x1)))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__sqr(mark(z0)), x1)), a__dbl(mark(cons(sqr(z0), x1)))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(a__add(mark(z0), mark(z1)), x1)), a__dbl(mark(cons(add(z0, z1), x1)))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__dbl(mark(z0)), x1)), a__dbl(mark(cons(dbl(z0), x1)))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(a__first(mark(z0), mark(z1)), x1)), a__dbl(mark(cons(first(z0, z1), x1)))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__half(mark(z0)), x1)), a__dbl(mark(cons(half(z0), x1)))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(cons(mark(z0), z1), x1)), a__dbl(mark(cons(cons(z0, z1), x1)))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(cons(recip(mark(z0)), x1)), a__dbl(mark(cons(recip(z0), x1)))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(cons(s(mark(z0)), x1)), a__dbl(mark(cons(s(z0), x1)))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(cons(0, x1)), a__dbl(mark(cons(0, x1)))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(cons(nil, x1)), a__dbl(mark(cons(nil, x1)))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) 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c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), 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A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__terms(mark(z0)))), a__dbl(mark(dbl(terms(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__sqr(mark(z0)))), a__dbl(mark(dbl(sqr(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__add(mark(z0), mark(z1)))), a__dbl(mark(dbl(add(z0, z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__dbl(mark(z0)))), a__dbl(mark(dbl(dbl(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__first(mark(z0), mark(z1)))), a__dbl(mark(dbl(first(z0, z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__half(mark(z0)))), a__dbl(mark(dbl(half(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(cons(mark(z0), z1))), a__dbl(mark(dbl(cons(z0, z1))))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(a__dbl(recip(mark(z0)))), a__dbl(mark(dbl(recip(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(a__dbl(s(mark(z0)))), a__dbl(mark(dbl(s(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(a__dbl(0)), a__dbl(mark(dbl(0)))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(a__dbl(nil)), a__dbl(mark(dbl(nil)))), A__SQR(mark(dbl(nil)))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(first(mark(x0), mark(x1))), a__dbl(mark(first(x0, x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__terms(mark(z0)))), a__dbl(mark(first(x0, terms(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(first(x0, sqr(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(first(x0, add(z0, z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(first(x0, dbl(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(first(x0, first(z0, z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__half(mark(z0)))), a__dbl(mark(first(x0, half(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), cons(mark(z0), z1))), a__dbl(mark(first(x0, cons(z0, z1))))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), recip(mark(z0)))), a__dbl(mark(first(x0, recip(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), s(mark(z0)))), a__dbl(mark(first(x0, s(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(a__first(mark(x0), 0)), a__dbl(mark(first(x0, 0)))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(a__first(mark(x0), nil)), a__dbl(mark(first(x0, nil)))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__terms(mark(z0)), mark(x1))), a__dbl(mark(first(terms(z0), x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(first(sqr(z0), x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(add(z0, z1), x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(first(dbl(z0), x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(first(z0, z1), x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__half(mark(z0)), mark(x1))), a__dbl(mark(first(half(z0), x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(cons(mark(z0), z1), mark(x1))), a__dbl(mark(first(cons(z0, z1), x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__first(recip(mark(z0)), mark(x1))), a__dbl(mark(first(recip(z0), x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(a__first(s(mark(z0)), mark(x1))), a__dbl(mark(first(s(z0), x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(a__first(0, mark(x1))), a__dbl(mark(first(0, x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(a__first(nil, mark(x1))), a__dbl(mark(first(nil, x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(half(mark(x0))), a__dbl(mark(half(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(a__half(a__terms(mark(z0)))), a__dbl(mark(half(terms(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(a__half(a__sqr(mark(z0)))), a__dbl(mark(half(sqr(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__add(mark(z0), mark(z1)))), a__dbl(mark(half(add(z0, z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(a__half(a__dbl(mark(z0)))), a__dbl(mark(half(dbl(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__first(mark(z0), mark(z1)))), a__dbl(mark(half(first(z0, z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(a__half(a__half(mark(z0)))), a__dbl(mark(half(half(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(cons(mark(z0), z1))), a__dbl(mark(half(cons(z0, z1))))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(a__half(recip(mark(z0)))), a__dbl(mark(half(recip(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(a__half(s(mark(z0)))), a__dbl(mark(half(s(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(a__half(0)), a__dbl(mark(half(0)))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(a__half(nil)), a__dbl(mark(half(nil)))), A__SQR(mark(half(nil)))) A__SQR(s(cons(x0, x1))) -> c3(A__ADD(sqr(cons(mark(x0), x1)), a__dbl(mark(cons(x0, x1)))), A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__terms(mark(z0)), x1)), a__dbl(mark(cons(terms(z0), x1)))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__sqr(mark(z0)), x1)), a__dbl(mark(cons(sqr(z0), x1)))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(a__add(mark(z0), mark(z1)), x1)), a__dbl(mark(cons(add(z0, z1), x1)))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__dbl(mark(z0)), x1)), a__dbl(mark(cons(dbl(z0), x1)))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(a__first(mark(z0), mark(z1)), x1)), a__dbl(mark(cons(first(z0, z1), x1)))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__half(mark(z0)), x1)), a__dbl(mark(cons(half(z0), x1)))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(cons(mark(z0), z1), x1)), a__dbl(mark(cons(cons(z0, z1), x1)))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(cons(recip(mark(z0)), x1)), a__dbl(mark(cons(recip(z0), x1)))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(cons(s(mark(z0)), x1)), a__dbl(mark(cons(s(z0), x1)))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(cons(0, x1)), a__dbl(mark(cons(0, x1)))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(cons(nil, x1)), a__dbl(mark(cons(nil, x1)))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__terms(mark(z0)))), a__dbl(mark(dbl(terms(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__sqr(mark(z0)))), a__dbl(mark(dbl(sqr(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__add(mark(z0), mark(z1)))), a__dbl(mark(dbl(add(z0, z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__dbl(mark(z0)))), a__dbl(mark(dbl(dbl(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__first(mark(z0), mark(z1)))), a__dbl(mark(dbl(first(z0, z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__half(mark(z0)))), a__dbl(mark(dbl(half(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(cons(mark(z0), z1))), a__dbl(mark(dbl(cons(z0, z1))))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(a__dbl(recip(mark(z0)))), a__dbl(mark(dbl(recip(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(a__dbl(s(mark(z0)))), a__dbl(mark(dbl(s(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(a__dbl(0)), a__dbl(mark(dbl(0)))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(a__dbl(nil)), a__dbl(mark(dbl(nil)))), A__SQR(mark(dbl(nil)))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(first(mark(x0), mark(x1))), a__dbl(mark(first(x0, x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__terms(mark(z0)))), a__dbl(mark(first(x0, terms(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(first(x0, sqr(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(first(x0, add(z0, z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(first(x0, dbl(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(first(x0, first(z0, z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__half(mark(z0)))), a__dbl(mark(first(x0, half(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), cons(mark(z0), z1))), a__dbl(mark(first(x0, cons(z0, z1))))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), recip(mark(z0)))), a__dbl(mark(first(x0, recip(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), s(mark(z0)))), a__dbl(mark(first(x0, s(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(a__first(mark(x0), 0)), a__dbl(mark(first(x0, 0)))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(a__first(mark(x0), nil)), a__dbl(mark(first(x0, nil)))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__terms(mark(z0)), mark(x1))), a__dbl(mark(first(terms(z0), x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(first(sqr(z0), x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(add(z0, z1), x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(first(dbl(z0), x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(first(z0, z1), x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__half(mark(z0)), mark(x1))), a__dbl(mark(first(half(z0), x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(cons(mark(z0), z1), mark(x1))), a__dbl(mark(first(cons(z0, z1), x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__first(recip(mark(z0)), mark(x1))), a__dbl(mark(first(recip(z0), x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(a__first(s(mark(z0)), mark(x1))), a__dbl(mark(first(s(z0), x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(a__first(0, mark(x1))), a__dbl(mark(first(0, x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(a__first(nil, mark(x1))), a__dbl(mark(first(nil, x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(half(mark(x0))), a__dbl(mark(half(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(a__half(a__terms(mark(z0)))), a__dbl(mark(half(terms(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(a__half(a__sqr(mark(z0)))), a__dbl(mark(half(sqr(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__add(mark(z0), mark(z1)))), a__dbl(mark(half(add(z0, z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(a__half(a__dbl(mark(z0)))), a__dbl(mark(half(dbl(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__first(mark(z0), mark(z1)))), a__dbl(mark(half(first(z0, z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(a__half(a__half(mark(z0)))), a__dbl(mark(half(half(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(cons(mark(z0), z1))), a__dbl(mark(half(cons(z0, z1))))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(a__half(recip(mark(z0)))), a__dbl(mark(half(recip(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(a__half(s(mark(z0)))), a__dbl(mark(half(s(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(a__half(0)), a__dbl(mark(half(0)))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(a__half(nil)), a__dbl(mark(half(nil)))), A__SQR(mark(half(nil)))) A__SQR(s(cons(x0, x1))) -> c3(A__ADD(sqr(cons(mark(x0), x1)), a__dbl(mark(cons(x0, x1)))), A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__terms(mark(z0)), x1)), a__dbl(mark(cons(terms(z0), x1)))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__sqr(mark(z0)), x1)), a__dbl(mark(cons(sqr(z0), x1)))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(a__add(mark(z0), mark(z1)), x1)), a__dbl(mark(cons(add(z0, z1), x1)))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__dbl(mark(z0)), x1)), a__dbl(mark(cons(dbl(z0), x1)))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(a__first(mark(z0), mark(z1)), x1)), a__dbl(mark(cons(first(z0, z1), x1)))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__half(mark(z0)), x1)), a__dbl(mark(cons(half(z0), x1)))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(cons(mark(z0), z1), x1)), a__dbl(mark(cons(cons(z0, z1), x1)))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(cons(recip(mark(z0)), x1)), a__dbl(mark(cons(recip(z0), x1)))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(cons(s(mark(z0)), x1)), a__dbl(mark(cons(s(z0), x1)))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(cons(0, x1)), a__dbl(mark(cons(0, x1)))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(cons(nil, x1)), a__dbl(mark(cons(nil, x1)))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (239) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__terms(mark(z0)))), a__dbl(mark(dbl(terms(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__sqr(mark(z0)))), a__dbl(mark(dbl(sqr(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__add(mark(z0), mark(z1)))), a__dbl(mark(dbl(add(z0, z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__dbl(mark(z0)))), a__dbl(mark(dbl(dbl(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__first(mark(z0), mark(z1)))), a__dbl(mark(dbl(first(z0, z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__half(mark(z0)))), a__dbl(mark(dbl(half(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(cons(mark(z0), z1))), a__dbl(mark(dbl(cons(z0, z1))))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(a__dbl(recip(mark(z0)))), a__dbl(mark(dbl(recip(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(a__dbl(s(mark(z0)))), a__dbl(mark(dbl(s(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(a__dbl(0)), a__dbl(mark(dbl(0)))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(a__dbl(nil)), a__dbl(mark(dbl(nil)))), A__SQR(mark(dbl(nil)))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(first(mark(x0), mark(x1))), a__dbl(mark(first(x0, x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__terms(mark(z0)))), a__dbl(mark(first(x0, terms(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(first(x0, sqr(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(first(x0, add(z0, z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(first(x0, dbl(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(first(x0, first(z0, z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__half(mark(z0)))), a__dbl(mark(first(x0, half(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), cons(mark(z0), z1))), a__dbl(mark(first(x0, cons(z0, z1))))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), recip(mark(z0)))), a__dbl(mark(first(x0, recip(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), s(mark(z0)))), a__dbl(mark(first(x0, s(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(a__first(mark(x0), 0)), a__dbl(mark(first(x0, 0)))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(a__first(mark(x0), nil)), a__dbl(mark(first(x0, nil)))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__terms(mark(z0)), mark(x1))), a__dbl(mark(first(terms(z0), x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(first(sqr(z0), x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(add(z0, z1), x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(first(dbl(z0), x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(first(z0, z1), x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__half(mark(z0)), mark(x1))), a__dbl(mark(first(half(z0), x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(cons(mark(z0), z1), mark(x1))), a__dbl(mark(first(cons(z0, z1), x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__first(recip(mark(z0)), mark(x1))), a__dbl(mark(first(recip(z0), x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(a__first(s(mark(z0)), mark(x1))), a__dbl(mark(first(s(z0), x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(a__first(0, mark(x1))), a__dbl(mark(first(0, x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(a__first(nil, mark(x1))), a__dbl(mark(first(nil, x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(half(mark(x0))), a__dbl(mark(half(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(a__half(a__terms(mark(z0)))), a__dbl(mark(half(terms(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(a__half(a__sqr(mark(z0)))), a__dbl(mark(half(sqr(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__add(mark(z0), mark(z1)))), a__dbl(mark(half(add(z0, z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(a__half(a__dbl(mark(z0)))), a__dbl(mark(half(dbl(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__first(mark(z0), mark(z1)))), a__dbl(mark(half(first(z0, z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(a__half(a__half(mark(z0)))), a__dbl(mark(half(half(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(cons(mark(z0), z1))), a__dbl(mark(half(cons(z0, z1))))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(a__half(recip(mark(z0)))), a__dbl(mark(half(recip(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(a__half(s(mark(z0)))), a__dbl(mark(half(s(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(a__half(0)), a__dbl(mark(half(0)))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(a__half(nil)), a__dbl(mark(half(nil)))), A__SQR(mark(half(nil)))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__terms(mark(z0)), x1)), a__dbl(mark(cons(terms(z0), x1)))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__sqr(mark(z0)), x1)), a__dbl(mark(cons(sqr(z0), x1)))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(a__add(mark(z0), mark(z1)), x1)), a__dbl(mark(cons(add(z0, z1), x1)))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__dbl(mark(z0)), x1)), a__dbl(mark(cons(dbl(z0), x1)))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(a__first(mark(z0), mark(z1)), x1)), a__dbl(mark(cons(first(z0, z1), x1)))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__half(mark(z0)), x1)), a__dbl(mark(cons(half(z0), x1)))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(cons(mark(z0), z1), x1)), a__dbl(mark(cons(cons(z0, z1), x1)))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(cons(recip(mark(z0)), x1)), a__dbl(mark(cons(recip(z0), x1)))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(cons(s(mark(z0)), x1)), a__dbl(mark(cons(s(z0), x1)))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(cons(0, x1)), a__dbl(mark(cons(0, x1)))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(cons(nil, x1)), a__dbl(mark(cons(nil, x1)))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> 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MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, 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c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__terms(mark(z0)))), a__dbl(mark(dbl(terms(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__sqr(mark(z0)))), a__dbl(mark(dbl(sqr(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__add(mark(z0), mark(z1)))), a__dbl(mark(dbl(add(z0, z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__dbl(mark(z0)))), a__dbl(mark(dbl(dbl(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__first(mark(z0), mark(z1)))), a__dbl(mark(dbl(first(z0, z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__half(mark(z0)))), a__dbl(mark(dbl(half(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(cons(mark(z0), z1))), a__dbl(mark(dbl(cons(z0, z1))))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(a__dbl(recip(mark(z0)))), a__dbl(mark(dbl(recip(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(a__dbl(s(mark(z0)))), a__dbl(mark(dbl(s(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(a__dbl(0)), a__dbl(mark(dbl(0)))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(a__dbl(nil)), a__dbl(mark(dbl(nil)))), A__SQR(mark(dbl(nil)))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(first(mark(x0), mark(x1))), a__dbl(mark(first(x0, x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__terms(mark(z0)))), a__dbl(mark(first(x0, terms(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(first(x0, sqr(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(first(x0, add(z0, z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(first(x0, dbl(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(first(x0, first(z0, z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__half(mark(z0)))), a__dbl(mark(first(x0, half(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), cons(mark(z0), z1))), a__dbl(mark(first(x0, cons(z0, z1))))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), recip(mark(z0)))), a__dbl(mark(first(x0, recip(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), s(mark(z0)))), a__dbl(mark(first(x0, s(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(a__first(mark(x0), 0)), a__dbl(mark(first(x0, 0)))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(a__first(mark(x0), nil)), a__dbl(mark(first(x0, nil)))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__terms(mark(z0)), mark(x1))), a__dbl(mark(first(terms(z0), x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(first(sqr(z0), x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(add(z0, z1), x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(first(dbl(z0), x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(first(z0, z1), x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__half(mark(z0)), mark(x1))), a__dbl(mark(first(half(z0), x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(cons(mark(z0), z1), mark(x1))), a__dbl(mark(first(cons(z0, z1), x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__first(recip(mark(z0)), mark(x1))), a__dbl(mark(first(recip(z0), x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(a__first(s(mark(z0)), mark(x1))), a__dbl(mark(first(s(z0), x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(a__first(0, mark(x1))), a__dbl(mark(first(0, x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(a__first(nil, mark(x1))), a__dbl(mark(first(nil, x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(half(mark(x0))), a__dbl(mark(half(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(a__half(a__terms(mark(z0)))), a__dbl(mark(half(terms(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(a__half(a__sqr(mark(z0)))), a__dbl(mark(half(sqr(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__add(mark(z0), mark(z1)))), a__dbl(mark(half(add(z0, z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(a__half(a__dbl(mark(z0)))), a__dbl(mark(half(dbl(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__first(mark(z0), mark(z1)))), a__dbl(mark(half(first(z0, z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(a__half(a__half(mark(z0)))), a__dbl(mark(half(half(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(cons(mark(z0), z1))), a__dbl(mark(half(cons(z0, z1))))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(a__half(recip(mark(z0)))), a__dbl(mark(half(recip(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(a__half(s(mark(z0)))), a__dbl(mark(half(s(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(a__half(0)), a__dbl(mark(half(0)))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(a__half(nil)), a__dbl(mark(half(nil)))), A__SQR(mark(half(nil)))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__terms(mark(z0)), x1)), a__dbl(mark(cons(terms(z0), x1)))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__sqr(mark(z0)), x1)), a__dbl(mark(cons(sqr(z0), x1)))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(a__add(mark(z0), mark(z1)), x1)), a__dbl(mark(cons(add(z0, z1), x1)))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__dbl(mark(z0)), x1)), a__dbl(mark(cons(dbl(z0), x1)))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(a__first(mark(z0), mark(z1)), x1)), a__dbl(mark(cons(first(z0, z1), x1)))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__half(mark(z0)), x1)), a__dbl(mark(cons(half(z0), x1)))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(cons(mark(z0), z1), x1)), a__dbl(mark(cons(cons(z0, z1), x1)))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(cons(recip(mark(z0)), x1)), a__dbl(mark(cons(recip(z0), x1)))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(cons(s(mark(z0)), x1)), a__dbl(mark(cons(s(z0), x1)))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(cons(0, x1)), a__dbl(mark(cons(0, x1)))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(cons(nil, x1)), a__dbl(mark(cons(nil, x1)))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (241) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) by A__SQR(s(recip(x0))) -> c3(A__ADD(a__sqr(recip(mark(x0))), dbl(mark(recip(x0)))), A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__ADD(sqr(recip(mark(x0))), a__dbl(mark(recip(x0)))), A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(recip(a__terms(mark(z0)))), a__dbl(mark(recip(terms(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(recip(a__sqr(mark(z0)))), a__dbl(mark(recip(sqr(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(recip(a__add(mark(z0), mark(z1)))), a__dbl(mark(recip(add(z0, z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(recip(a__dbl(mark(z0)))), a__dbl(mark(recip(dbl(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(recip(a__first(mark(z0), mark(z1)))), a__dbl(mark(recip(first(z0, z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(recip(a__half(mark(z0)))), a__dbl(mark(recip(half(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(recip(cons(mark(z0), z1))), a__dbl(mark(recip(cons(z0, z1))))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(recip(recip(mark(z0)))), a__dbl(mark(recip(recip(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(recip(s(mark(z0)))), a__dbl(mark(recip(s(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(recip(0)), a__dbl(mark(recip(0)))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(recip(nil)), a__dbl(mark(recip(nil)))), A__SQR(mark(recip(nil))), MARK(recip(nil))) ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__terms(mark(z0)))), a__dbl(mark(dbl(terms(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__sqr(mark(z0)))), a__dbl(mark(dbl(sqr(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__add(mark(z0), mark(z1)))), a__dbl(mark(dbl(add(z0, z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__dbl(mark(z0)))), a__dbl(mark(dbl(dbl(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__first(mark(z0), mark(z1)))), a__dbl(mark(dbl(first(z0, z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__half(mark(z0)))), a__dbl(mark(dbl(half(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(cons(mark(z0), z1))), a__dbl(mark(dbl(cons(z0, z1))))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(a__dbl(recip(mark(z0)))), a__dbl(mark(dbl(recip(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(a__dbl(s(mark(z0)))), a__dbl(mark(dbl(s(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(a__dbl(0)), a__dbl(mark(dbl(0)))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(a__dbl(nil)), a__dbl(mark(dbl(nil)))), A__SQR(mark(dbl(nil)))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(first(mark(x0), mark(x1))), a__dbl(mark(first(x0, x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__terms(mark(z0)))), a__dbl(mark(first(x0, terms(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(first(x0, sqr(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(first(x0, add(z0, z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(first(x0, dbl(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(first(x0, first(z0, z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__half(mark(z0)))), a__dbl(mark(first(x0, half(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), cons(mark(z0), z1))), a__dbl(mark(first(x0, cons(z0, z1))))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), recip(mark(z0)))), a__dbl(mark(first(x0, recip(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), s(mark(z0)))), a__dbl(mark(first(x0, s(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(a__first(mark(x0), 0)), a__dbl(mark(first(x0, 0)))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(a__first(mark(x0), nil)), a__dbl(mark(first(x0, nil)))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__terms(mark(z0)), mark(x1))), a__dbl(mark(first(terms(z0), x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(first(sqr(z0), x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(add(z0, z1), x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(first(dbl(z0), x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(first(z0, z1), x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__half(mark(z0)), mark(x1))), a__dbl(mark(first(half(z0), x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(cons(mark(z0), z1), mark(x1))), a__dbl(mark(first(cons(z0, z1), x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__first(recip(mark(z0)), mark(x1))), a__dbl(mark(first(recip(z0), x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(a__first(s(mark(z0)), mark(x1))), a__dbl(mark(first(s(z0), x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(a__first(0, mark(x1))), a__dbl(mark(first(0, x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(a__first(nil, mark(x1))), a__dbl(mark(first(nil, x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(half(mark(x0))), a__dbl(mark(half(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(a__half(a__terms(mark(z0)))), a__dbl(mark(half(terms(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(a__half(a__sqr(mark(z0)))), a__dbl(mark(half(sqr(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__add(mark(z0), mark(z1)))), a__dbl(mark(half(add(z0, z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(a__half(a__dbl(mark(z0)))), a__dbl(mark(half(dbl(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__first(mark(z0), mark(z1)))), a__dbl(mark(half(first(z0, z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(a__half(a__half(mark(z0)))), a__dbl(mark(half(half(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(cons(mark(z0), z1))), a__dbl(mark(half(cons(z0, z1))))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(a__half(recip(mark(z0)))), a__dbl(mark(half(recip(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(a__half(s(mark(z0)))), a__dbl(mark(half(s(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(a__half(0)), a__dbl(mark(half(0)))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(a__half(nil)), a__dbl(mark(half(nil)))), A__SQR(mark(half(nil)))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__terms(mark(z0)), x1)), a__dbl(mark(cons(terms(z0), x1)))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__sqr(mark(z0)), x1)), a__dbl(mark(cons(sqr(z0), x1)))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(a__add(mark(z0), mark(z1)), x1)), a__dbl(mark(cons(add(z0, z1), x1)))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__dbl(mark(z0)), x1)), a__dbl(mark(cons(dbl(z0), x1)))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(a__first(mark(z0), mark(z1)), x1)), a__dbl(mark(cons(first(z0, z1), x1)))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__half(mark(z0)), x1)), a__dbl(mark(cons(half(z0), x1)))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(cons(mark(z0), z1), x1)), a__dbl(mark(cons(cons(z0, z1), x1)))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(cons(recip(mark(z0)), x1)), a__dbl(mark(cons(recip(z0), x1)))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(cons(s(mark(z0)), x1)), a__dbl(mark(cons(s(z0), x1)))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(cons(0, x1)), a__dbl(mark(cons(0, x1)))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(cons(nil, x1)), a__dbl(mark(cons(nil, x1)))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(recip(x0))) -> c3(A__ADD(sqr(recip(mark(x0))), a__dbl(mark(recip(x0)))), A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(recip(a__terms(mark(z0)))), a__dbl(mark(recip(terms(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(recip(a__sqr(mark(z0)))), a__dbl(mark(recip(sqr(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(recip(a__add(mark(z0), mark(z1)))), a__dbl(mark(recip(add(z0, z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(recip(a__dbl(mark(z0)))), a__dbl(mark(recip(dbl(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(recip(a__first(mark(z0), mark(z1)))), a__dbl(mark(recip(first(z0, z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(recip(a__half(mark(z0)))), a__dbl(mark(recip(half(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(recip(cons(mark(z0), z1))), a__dbl(mark(recip(cons(z0, z1))))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(recip(recip(mark(z0)))), a__dbl(mark(recip(recip(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(recip(s(mark(z0)))), a__dbl(mark(recip(s(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(recip(0)), a__dbl(mark(recip(0)))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(recip(nil)), a__dbl(mark(recip(nil)))), A__SQR(mark(recip(nil))), MARK(recip(nil))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__terms(mark(z0)))), a__dbl(mark(dbl(terms(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__sqr(mark(z0)))), a__dbl(mark(dbl(sqr(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__add(mark(z0), mark(z1)))), a__dbl(mark(dbl(add(z0, z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__dbl(mark(z0)))), a__dbl(mark(dbl(dbl(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__first(mark(z0), mark(z1)))), a__dbl(mark(dbl(first(z0, z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__half(mark(z0)))), a__dbl(mark(dbl(half(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(cons(mark(z0), z1))), a__dbl(mark(dbl(cons(z0, z1))))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(a__dbl(recip(mark(z0)))), a__dbl(mark(dbl(recip(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(a__dbl(s(mark(z0)))), a__dbl(mark(dbl(s(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(a__dbl(0)), a__dbl(mark(dbl(0)))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(a__dbl(nil)), a__dbl(mark(dbl(nil)))), A__SQR(mark(dbl(nil)))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(first(mark(x0), mark(x1))), a__dbl(mark(first(x0, x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__terms(mark(z0)))), a__dbl(mark(first(x0, terms(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(first(x0, sqr(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(first(x0, add(z0, z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(first(x0, dbl(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(first(x0, first(z0, z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__half(mark(z0)))), a__dbl(mark(first(x0, half(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), cons(mark(z0), z1))), a__dbl(mark(first(x0, cons(z0, z1))))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), recip(mark(z0)))), a__dbl(mark(first(x0, recip(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), s(mark(z0)))), a__dbl(mark(first(x0, s(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(a__first(mark(x0), 0)), a__dbl(mark(first(x0, 0)))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(a__first(mark(x0), nil)), a__dbl(mark(first(x0, nil)))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__terms(mark(z0)), mark(x1))), a__dbl(mark(first(terms(z0), x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(first(sqr(z0), x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(add(z0, z1), x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(first(dbl(z0), x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(first(z0, z1), x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__half(mark(z0)), mark(x1))), a__dbl(mark(first(half(z0), x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(cons(mark(z0), z1), mark(x1))), a__dbl(mark(first(cons(z0, z1), x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__first(recip(mark(z0)), mark(x1))), a__dbl(mark(first(recip(z0), x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(a__first(s(mark(z0)), mark(x1))), a__dbl(mark(first(s(z0), x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(a__first(0, mark(x1))), a__dbl(mark(first(0, x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(a__first(nil, mark(x1))), a__dbl(mark(first(nil, x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(half(mark(x0))), a__dbl(mark(half(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(a__half(a__terms(mark(z0)))), a__dbl(mark(half(terms(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(a__half(a__sqr(mark(z0)))), a__dbl(mark(half(sqr(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__add(mark(z0), mark(z1)))), a__dbl(mark(half(add(z0, z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(a__half(a__dbl(mark(z0)))), a__dbl(mark(half(dbl(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__first(mark(z0), mark(z1)))), a__dbl(mark(half(first(z0, z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(a__half(a__half(mark(z0)))), a__dbl(mark(half(half(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(cons(mark(z0), z1))), a__dbl(mark(half(cons(z0, z1))))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(a__half(recip(mark(z0)))), a__dbl(mark(half(recip(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(a__half(s(mark(z0)))), a__dbl(mark(half(s(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(a__half(0)), a__dbl(mark(half(0)))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(a__half(nil)), a__dbl(mark(half(nil)))), A__SQR(mark(half(nil)))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__terms(mark(z0)), x1)), a__dbl(mark(cons(terms(z0), x1)))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__sqr(mark(z0)), x1)), a__dbl(mark(cons(sqr(z0), x1)))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(a__add(mark(z0), mark(z1)), x1)), a__dbl(mark(cons(add(z0, z1), x1)))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__dbl(mark(z0)), x1)), a__dbl(mark(cons(dbl(z0), x1)))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(a__first(mark(z0), mark(z1)), x1)), a__dbl(mark(cons(first(z0, z1), x1)))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__half(mark(z0)), x1)), a__dbl(mark(cons(half(z0), x1)))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(cons(mark(z0), z1), x1)), a__dbl(mark(cons(cons(z0, z1), x1)))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(cons(recip(mark(z0)), x1)), a__dbl(mark(cons(recip(z0), x1)))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(cons(s(mark(z0)), x1)), a__dbl(mark(cons(s(z0), x1)))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(cons(0, x1)), a__dbl(mark(cons(0, x1)))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(cons(nil, x1)), a__dbl(mark(cons(nil, x1)))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(recip(x0))) -> c3(A__ADD(sqr(recip(mark(x0))), a__dbl(mark(recip(x0)))), A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(recip(a__terms(mark(z0)))), a__dbl(mark(recip(terms(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(recip(a__sqr(mark(z0)))), a__dbl(mark(recip(sqr(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(recip(a__add(mark(z0), mark(z1)))), a__dbl(mark(recip(add(z0, z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(recip(a__dbl(mark(z0)))), a__dbl(mark(recip(dbl(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(recip(a__first(mark(z0), mark(z1)))), a__dbl(mark(recip(first(z0, z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(recip(a__half(mark(z0)))), a__dbl(mark(recip(half(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(recip(cons(mark(z0), z1))), a__dbl(mark(recip(cons(z0, z1))))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(recip(recip(mark(z0)))), a__dbl(mark(recip(recip(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(recip(s(mark(z0)))), a__dbl(mark(recip(s(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(recip(0)), a__dbl(mark(recip(0)))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(recip(nil)), a__dbl(mark(recip(nil)))), A__SQR(mark(recip(nil))), MARK(recip(nil))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (243) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__half(0) -> 0 a__half(s(0)) -> 0 a__half(s(s(z0))) -> s(a__half(mark(z0))) a__half(dbl(z0)) -> mark(z0) a__half(z0) -> half(z0) 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(half(z0)) -> a__half(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__terms(mark(z0)))), a__dbl(mark(dbl(terms(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__sqr(mark(z0)))), a__dbl(mark(dbl(sqr(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__add(mark(z0), mark(z1)))), a__dbl(mark(dbl(add(z0, z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__dbl(mark(z0)))), a__dbl(mark(dbl(dbl(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__first(mark(z0), mark(z1)))), a__dbl(mark(dbl(first(z0, z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__half(mark(z0)))), a__dbl(mark(dbl(half(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(cons(mark(z0), z1))), a__dbl(mark(dbl(cons(z0, z1))))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(a__dbl(recip(mark(z0)))), a__dbl(mark(dbl(recip(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(a__dbl(s(mark(z0)))), a__dbl(mark(dbl(s(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(a__dbl(0)), a__dbl(mark(dbl(0)))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(a__dbl(nil)), a__dbl(mark(dbl(nil)))), A__SQR(mark(dbl(nil)))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(first(mark(x0), mark(x1))), a__dbl(mark(first(x0, x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__terms(mark(z0)))), a__dbl(mark(first(x0, terms(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(first(x0, sqr(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(first(x0, add(z0, z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(first(x0, dbl(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(first(x0, first(z0, z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__half(mark(z0)))), a__dbl(mark(first(x0, half(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), cons(mark(z0), z1))), a__dbl(mark(first(x0, cons(z0, z1))))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), recip(mark(z0)))), a__dbl(mark(first(x0, recip(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), s(mark(z0)))), a__dbl(mark(first(x0, s(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(a__first(mark(x0), 0)), a__dbl(mark(first(x0, 0)))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(a__first(mark(x0), nil)), a__dbl(mark(first(x0, nil)))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__terms(mark(z0)), mark(x1))), a__dbl(mark(first(terms(z0), x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(first(sqr(z0), x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(add(z0, z1), x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(first(dbl(z0), x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(first(z0, z1), x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__half(mark(z0)), mark(x1))), a__dbl(mark(first(half(z0), x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(cons(mark(z0), z1), mark(x1))), a__dbl(mark(first(cons(z0, z1), x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__first(recip(mark(z0)), mark(x1))), a__dbl(mark(first(recip(z0), x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(a__first(s(mark(z0)), mark(x1))), a__dbl(mark(first(s(z0), x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(a__first(0, mark(x1))), a__dbl(mark(first(0, x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(a__first(nil, mark(x1))), a__dbl(mark(first(nil, x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(half(mark(x0))), a__dbl(mark(half(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(a__half(a__terms(mark(z0)))), a__dbl(mark(half(terms(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(a__half(a__sqr(mark(z0)))), a__dbl(mark(half(sqr(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__add(mark(z0), mark(z1)))), a__dbl(mark(half(add(z0, z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(a__half(a__dbl(mark(z0)))), a__dbl(mark(half(dbl(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__first(mark(z0), mark(z1)))), a__dbl(mark(half(first(z0, z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(a__half(a__half(mark(z0)))), a__dbl(mark(half(half(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(cons(mark(z0), z1))), a__dbl(mark(half(cons(z0, z1))))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(a__half(recip(mark(z0)))), a__dbl(mark(half(recip(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(a__half(s(mark(z0)))), a__dbl(mark(half(s(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(a__half(0)), a__dbl(mark(half(0)))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(a__half(nil)), a__dbl(mark(half(nil)))), A__SQR(mark(half(nil)))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__terms(mark(z0)), x1)), a__dbl(mark(cons(terms(z0), x1)))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__sqr(mark(z0)), x1)), a__dbl(mark(cons(sqr(z0), x1)))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(a__add(mark(z0), mark(z1)), x1)), a__dbl(mark(cons(add(z0, z1), x1)))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__dbl(mark(z0)), x1)), a__dbl(mark(cons(dbl(z0), x1)))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(a__first(mark(z0), mark(z1)), x1)), a__dbl(mark(cons(first(z0, z1), x1)))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__half(mark(z0)), x1)), a__dbl(mark(cons(half(z0), x1)))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(cons(mark(z0), z1), x1)), a__dbl(mark(cons(cons(z0, z1), x1)))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(cons(recip(mark(z0)), x1)), a__dbl(mark(cons(recip(z0), x1)))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(cons(s(mark(z0)), x1)), a__dbl(mark(cons(s(z0), x1)))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(cons(0, x1)), a__dbl(mark(cons(0, x1)))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(cons(nil, x1)), a__dbl(mark(cons(nil, x1)))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(recip(a__terms(mark(z0)))), a__dbl(mark(recip(terms(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(recip(a__sqr(mark(z0)))), a__dbl(mark(recip(sqr(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(recip(a__add(mark(z0), mark(z1)))), a__dbl(mark(recip(add(z0, z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(recip(a__dbl(mark(z0)))), a__dbl(mark(recip(dbl(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(recip(a__first(mark(z0), mark(z1)))), a__dbl(mark(recip(first(z0, z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(recip(a__half(mark(z0)))), a__dbl(mark(recip(half(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(recip(cons(mark(z0), z1))), a__dbl(mark(recip(cons(z0, z1))))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(recip(recip(mark(z0)))), a__dbl(mark(recip(recip(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(recip(s(mark(z0)))), a__dbl(mark(recip(s(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(recip(0)), a__dbl(mark(recip(0)))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(recip(nil)), a__dbl(mark(recip(nil)))), A__SQR(mark(recip(nil))), MARK(recip(nil))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) A__HALF(dbl(z0)) -> c19(MARK(z0)) MARK(cons(z0, z1)) -> c29(MARK(z0)) MARK(recip(z0)) -> c30(MARK(z0)) MARK(s(z0)) -> c31(MARK(z0)) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), MARK(s(z0))) A__TERMS(cons(z0, z1)) -> c(MARK(cons(z0, z1))) A__TERMS(recip(z0)) -> c(MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(mark(half(z0))), a__dbl(a__half(mark(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c4(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(mark(half(z0)))), A__DBL(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(half(z0))) -> c7(A__DBL(a__half(mark(z0))), MARK(half(z0))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), half(z0)) -> c10(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(half(z0)), x1) -> c10(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), half(z0)) -> c11(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(half(z0)), x1) -> c11(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) A__HALF(s(s(terms(z0)))) -> c18(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) A__HALF(s(s(sqr(z0)))) -> c18(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) A__HALF(s(s(add(z0, z1)))) -> c18(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__HALF(s(s(dbl(z0)))) -> c18(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) A__HALF(s(s(first(z0, z1)))) -> c18(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__HALF(s(s(half(z0)))) -> c18(A__HALF(a__half(mark(z0))), MARK(half(z0))) A__HALF(s(s(s(z0)))) -> c18(A__HALF(s(mark(z0))), MARK(s(z0))) A__HALF(s(s(cons(z0, z1)))) -> c18(MARK(cons(z0, z1))) A__HALF(s(s(recip(z0)))) -> c18(MARK(recip(z0))) MARK(terms(terms(z0))) -> c21(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c21(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c21(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c21(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c21(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(half(z0))) -> c21(A__TERMS(a__half(mark(z0))), MARK(half(z0))) MARK(terms(cons(z0, z1))) -> c21(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c21(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c21(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c22(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c22(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c22(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c22(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c22(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(half(z0))) -> c22(A__SQR(a__half(mark(z0))), MARK(half(z0))) MARK(sqr(s(z0))) -> c22(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c22(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c22(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c23(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c23(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c23(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c23(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c23(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, half(z0))) -> c23(A__ADD(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c23(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c23(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c23(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c23(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c23(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c23(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c23(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c23(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c23(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c23(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(half(z0), x1)) -> c23(A__ADD(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(add(s(z0), x1)) -> c23(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c23(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c23(MARK(recip(z0))) MARK(add(0, x1)) -> c23(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c24(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c24(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c24(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c24(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c24(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, half(z0))) -> c24(A__ADD(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(add(x0, cons(z0, z1))) -> c24(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c24(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c24(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c24(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c24(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c24(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c24(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c24(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(half(z0), x1)) -> c24(A__ADD(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c24(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c24(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c24(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c24(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c24(MARK(x1)) MARK(add(recip(z0), x1)) -> c24(MARK(x1)) MARK(add(nil, x1)) -> c24(MARK(x1)) MARK(dbl(terms(z0))) -> c25(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c25(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c25(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c25(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c25(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(half(z0))) -> c25(A__DBL(a__half(mark(z0))), MARK(half(z0))) MARK(dbl(s(z0))) -> c25(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c25(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c25(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c26(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c26(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c26(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c26(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c26(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, half(z0))) -> c26(A__FIRST(mark(x0), a__half(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c26(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c26(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c26(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c26(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c26(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c26(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(half(z0), x1)) -> c26(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(half(z0))) MARK(first(s(z0), x1)) -> c26(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c26(MARK(x0)) MARK(first(x0, s(z0))) -> c26(MARK(x0)) MARK(first(x0, 0)) -> c26(MARK(x0)) MARK(first(x0, nil)) -> c26(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c26(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c26(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c27(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c27(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c27(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c27(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c27(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, half(z0))) -> c27(A__FIRST(mark(x0), a__half(mark(z0))), MARK(half(z0))) MARK(first(x0, cons(z0, z1))) -> c27(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c27(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c27(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c27(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c27(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c27(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(half(z0), x1)) -> c27(A__FIRST(a__half(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c27(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c27(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c27(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c27(MARK(x1)) MARK(first(recip(z0), x1)) -> c27(MARK(x1)) MARK(first(0, x1)) -> c27(MARK(x1)) MARK(first(nil, x1)) -> c27(MARK(x1)) MARK(half(terms(z0))) -> c28(A__HALF(a__terms(mark(z0))), MARK(terms(z0))) MARK(half(sqr(z0))) -> c28(A__HALF(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(half(add(z0, z1))) -> c28(A__HALF(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(half(dbl(z0))) -> c28(A__HALF(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(half(first(z0, z1))) -> c28(A__HALF(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(half(half(z0))) -> c28(A__HALF(a__half(mark(z0))), MARK(half(z0))) MARK(half(s(z0))) -> c28(A__HALF(s(mark(z0))), MARK(s(z0))) MARK(half(cons(z0, z1))) -> c28(MARK(cons(z0, z1))) MARK(half(recip(z0))) -> c28(MARK(recip(z0))) A__TERMS(terms(terms(z0))) -> c(A__SQR(a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) A__TERMS(terms(sqr(z0))) -> c(A__SQR(a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) A__TERMS(terms(add(z0, z1))) -> c(A__SQR(a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) A__TERMS(terms(dbl(z0))) -> c(A__SQR(a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) A__TERMS(terms(first(z0, z1))) -> c(A__SQR(a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) A__TERMS(terms(half(z0))) -> c(A__SQR(a__terms(a__half(mark(z0)))), MARK(terms(half(z0)))) A__TERMS(terms(cons(z0, z1))) -> c(A__SQR(a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) A__TERMS(terms(recip(z0))) -> c(A__SQR(a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) A__TERMS(terms(s(z0))) -> c(A__SQR(a__terms(s(mark(z0)))), MARK(terms(s(z0)))) A__TERMS(terms(x0)) -> c(MARK(terms(x0))) A__TERMS(terms(0)) -> c(A__SQR(a__terms(0))) A__TERMS(terms(nil)) -> c(A__SQR(a__terms(nil))) A__TERMS(sqr(terms(z0))) -> c(A__SQR(a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) A__TERMS(sqr(sqr(z0))) -> c(A__SQR(a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) A__TERMS(sqr(add(z0, z1))) -> c(A__SQR(a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) A__TERMS(sqr(dbl(z0))) -> c(A__SQR(a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) A__TERMS(sqr(first(z0, z1))) -> c(A__SQR(a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) A__TERMS(sqr(half(z0))) -> c(A__SQR(a__sqr(a__half(mark(z0)))), MARK(sqr(half(z0)))) A__TERMS(sqr(cons(z0, z1))) -> c(A__SQR(a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) A__TERMS(sqr(recip(z0))) -> c(A__SQR(a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) A__TERMS(sqr(s(z0))) -> c(A__SQR(a__sqr(s(mark(z0)))), MARK(sqr(s(z0)))) A__TERMS(sqr(x0)) -> c(MARK(sqr(x0))) A__TERMS(sqr(0)) -> c(A__SQR(a__sqr(0))) A__TERMS(sqr(nil)) -> c(A__SQR(a__sqr(nil))) A__TERMS(add(x0, terms(z0))) -> c(A__SQR(a__add(mark(x0), a__terms(mark(z0)))), MARK(add(x0, terms(z0)))) A__TERMS(add(x0, sqr(z0))) -> c(A__SQR(a__add(mark(x0), a__sqr(mark(z0)))), MARK(add(x0, sqr(z0)))) A__TERMS(add(x0, add(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(x0, add(z0, z1)))) A__TERMS(add(x0, dbl(z0))) -> c(A__SQR(a__add(mark(x0), a__dbl(mark(z0)))), MARK(add(x0, dbl(z0)))) A__TERMS(add(x0, first(z0, z1))) -> c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) A__TERMS(add(x0, half(z0))) -> c(A__SQR(a__add(mark(x0), a__half(mark(z0)))), MARK(add(x0, half(z0)))) A__TERMS(add(x0, cons(z0, z1))) -> c(A__SQR(a__add(mark(x0), cons(mark(z0), z1))), MARK(add(x0, cons(z0, z1)))) A__TERMS(add(x0, recip(z0))) -> c(A__SQR(a__add(mark(x0), recip(mark(z0)))), MARK(add(x0, recip(z0)))) A__TERMS(add(x0, s(z0))) -> c(A__SQR(a__add(mark(x0), s(mark(z0)))), MARK(add(x0, s(z0)))) A__TERMS(add(x0, 0)) -> c(A__SQR(a__add(mark(x0), 0)), MARK(add(x0, 0))) A__TERMS(add(x0, nil)) -> c(A__SQR(a__add(mark(x0), nil)), MARK(add(x0, nil))) A__TERMS(add(terms(z0), x1)) -> c(A__SQR(a__add(a__terms(mark(z0)), mark(x1))), MARK(add(terms(z0), x1))) A__TERMS(add(sqr(z0), x1)) -> c(A__SQR(a__add(a__sqr(mark(z0)), mark(x1))), MARK(add(sqr(z0), x1))) A__TERMS(add(add(z0, z1), x1)) -> c(A__SQR(a__add(a__add(mark(z0), mark(z1)), mark(x1))), MARK(add(add(z0, z1), x1))) A__TERMS(add(dbl(z0), x1)) -> c(A__SQR(a__add(a__dbl(mark(z0)), mark(x1))), MARK(add(dbl(z0), x1))) A__TERMS(add(first(z0, z1), x1)) -> c(A__SQR(a__add(a__first(mark(z0), mark(z1)), mark(x1))), MARK(add(first(z0, z1), x1))) A__TERMS(add(half(z0), x1)) -> c(A__SQR(a__add(a__half(mark(z0)), mark(x1))), MARK(add(half(z0), x1))) A__TERMS(add(cons(z0, z1), x1)) -> c(A__SQR(a__add(cons(mark(z0), z1), mark(x1))), MARK(add(cons(z0, z1), x1))) A__TERMS(add(recip(z0), x1)) -> c(A__SQR(a__add(recip(mark(z0)), mark(x1))), MARK(add(recip(z0), x1))) A__TERMS(add(s(z0), x1)) -> c(A__SQR(a__add(s(mark(z0)), mark(x1))), MARK(add(s(z0), x1))) A__TERMS(add(0, x1)) -> c(A__SQR(a__add(0, mark(x1))), MARK(add(0, x1))) A__TERMS(add(nil, x1)) -> c(A__SQR(a__add(nil, mark(x1))), MARK(add(nil, x1))) A__TERMS(add(x0, x1)) -> c(MARK(add(x0, x1))) A__TERMS(dbl(terms(z0))) -> c(A__SQR(a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) A__TERMS(dbl(sqr(z0))) -> c(A__SQR(a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) A__TERMS(dbl(add(z0, z1))) -> c(A__SQR(a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) A__TERMS(dbl(dbl(z0))) -> c(A__SQR(a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) A__TERMS(dbl(first(z0, z1))) -> c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) A__TERMS(dbl(half(z0))) -> c(A__SQR(a__dbl(a__half(mark(z0)))), MARK(dbl(half(z0)))) A__TERMS(dbl(cons(z0, z1))) -> c(A__SQR(a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) A__TERMS(dbl(recip(z0))) -> c(A__SQR(a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) A__TERMS(dbl(s(z0))) -> c(A__SQR(a__dbl(s(mark(z0)))), MARK(dbl(s(z0)))) A__TERMS(dbl(x0)) -> c(MARK(dbl(x0))) A__TERMS(dbl(0)) -> c(A__SQR(a__dbl(0))) A__TERMS(dbl(nil)) -> c(A__SQR(a__dbl(nil))) A__TERMS(first(x0, terms(z0))) -> c(A__SQR(a__first(mark(x0), a__terms(mark(z0)))), MARK(first(x0, terms(z0)))) A__TERMS(first(x0, sqr(z0))) -> c(A__SQR(a__first(mark(x0), a__sqr(mark(z0)))), MARK(first(x0, sqr(z0)))) A__TERMS(first(x0, add(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__add(mark(z0), mark(z1)))), MARK(first(x0, add(z0, z1)))) A__TERMS(first(x0, dbl(z0))) -> c(A__SQR(a__first(mark(x0), a__dbl(mark(z0)))), MARK(first(x0, dbl(z0)))) A__TERMS(first(x0, first(z0, z1))) -> c(A__SQR(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) A__TERMS(first(x0, half(z0))) -> c(A__SQR(a__first(mark(x0), a__half(mark(z0)))), MARK(first(x0, half(z0)))) A__TERMS(first(x0, cons(z0, z1))) -> c(A__SQR(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) A__TERMS(first(x0, recip(z0))) -> c(A__SQR(a__first(mark(x0), recip(mark(z0)))), MARK(first(x0, recip(z0)))) A__TERMS(first(x0, s(z0))) -> c(A__SQR(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) A__TERMS(first(x0, 0)) -> c(A__SQR(a__first(mark(x0), 0)), MARK(first(x0, 0))) A__TERMS(first(x0, nil)) -> c(A__SQR(a__first(mark(x0), nil)), MARK(first(x0, nil))) A__TERMS(first(terms(z0), x1)) -> c(A__SQR(a__first(a__terms(mark(z0)), mark(x1))), MARK(first(terms(z0), x1))) A__TERMS(first(sqr(z0), x1)) -> c(A__SQR(a__first(a__sqr(mark(z0)), mark(x1))), MARK(first(sqr(z0), x1))) A__TERMS(first(add(z0, z1), x1)) -> c(A__SQR(a__first(a__add(mark(z0), mark(z1)), mark(x1))), MARK(first(add(z0, z1), x1))) A__TERMS(first(dbl(z0), x1)) -> c(A__SQR(a__first(a__dbl(mark(z0)), mark(x1))), MARK(first(dbl(z0), x1))) A__TERMS(first(first(z0, z1), x1)) -> c(A__SQR(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) A__TERMS(first(half(z0), x1)) -> c(A__SQR(a__first(a__half(mark(z0)), mark(x1))), MARK(first(half(z0), x1))) A__TERMS(first(cons(z0, z1), x1)) -> c(A__SQR(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) A__TERMS(first(recip(z0), x1)) -> c(A__SQR(a__first(recip(mark(z0)), mark(x1))), MARK(first(recip(z0), x1))) A__TERMS(first(s(z0), x1)) -> c(A__SQR(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) A__TERMS(first(0, x1)) -> c(A__SQR(a__first(0, mark(x1))), MARK(first(0, x1))) A__TERMS(first(nil, x1)) -> c(A__SQR(a__first(nil, mark(x1))), MARK(first(nil, x1))) A__TERMS(first(x0, x1)) -> c(MARK(first(x0, x1))) A__TERMS(half(terms(z0))) -> c(A__SQR(a__half(a__terms(mark(z0)))), MARK(half(terms(z0)))) A__TERMS(half(sqr(z0))) -> c(A__SQR(a__half(a__sqr(mark(z0)))), MARK(half(sqr(z0)))) A__TERMS(half(add(z0, z1))) -> c(A__SQR(a__half(a__add(mark(z0), mark(z1)))), MARK(half(add(z0, z1)))) A__TERMS(half(dbl(z0))) -> c(A__SQR(a__half(a__dbl(mark(z0)))), MARK(half(dbl(z0)))) A__TERMS(half(first(z0, z1))) -> c(A__SQR(a__half(a__first(mark(z0), mark(z1)))), MARK(half(first(z0, z1)))) A__TERMS(half(half(z0))) -> c(A__SQR(a__half(a__half(mark(z0)))), MARK(half(half(z0)))) A__TERMS(half(cons(z0, z1))) -> c(A__SQR(a__half(cons(mark(z0), z1))), MARK(half(cons(z0, z1)))) A__TERMS(half(recip(z0))) -> c(A__SQR(a__half(recip(mark(z0)))), MARK(half(recip(z0)))) A__TERMS(half(s(z0))) -> c(A__SQR(a__half(s(mark(z0)))), MARK(half(s(z0)))) A__TERMS(half(x0)) -> c(MARK(half(x0))) A__TERMS(half(0)) -> c(A__SQR(a__half(0))) A__TERMS(half(nil)) -> c(A__SQR(a__half(nil))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(mark(half(z0))), dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), dbl(mark(half(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(mark(terms(x0))), a__dbl(terms(mark(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(mark(terms(terms(z0)))), a__dbl(a__terms(a__terms(mark(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(terms(sqr(z0)))), a__dbl(a__terms(a__sqr(mark(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(add(z0, z1)))), a__dbl(a__terms(a__add(mark(z0), mark(z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(terms(dbl(z0)))), a__dbl(a__terms(a__dbl(mark(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(first(z0, z1)))), a__dbl(a__terms(a__first(mark(z0), mark(z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(mark(terms(half(z0)))), a__dbl(a__terms(a__half(mark(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(terms(cons(z0, z1)))), a__dbl(a__terms(cons(mark(z0), z1)))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(mark(terms(recip(z0)))), a__dbl(a__terms(recip(mark(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(mark(terms(s(z0)))), a__dbl(a__terms(s(mark(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(z0))) -> c3(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(a__terms(mark(z0)))), A__SQR(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(mark(terms(0))), a__dbl(a__terms(0))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(mark(terms(nil))), a__dbl(a__terms(nil))), A__SQR(mark(terms(nil)))) A__SQR(s(terms(x0))) -> c3(A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(mark(sqr(x0))), a__dbl(sqr(mark(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(sqr(z0)))), a__dbl(a__sqr(a__sqr(mark(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(terms(z0)))), a__dbl(a__sqr(a__terms(mark(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(add(z0, z1)))), a__dbl(a__sqr(a__add(mark(z0), mark(z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(dbl(z0)))), a__dbl(a__sqr(a__dbl(mark(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(first(z0, z1)))), a__dbl(a__sqr(a__first(mark(z0), mark(z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(half(z0)))), a__dbl(a__sqr(a__half(mark(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(sqr(cons(z0, z1)))), a__dbl(a__sqr(cons(mark(z0), z1)))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(recip(z0)))), a__dbl(a__sqr(recip(mark(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(mark(sqr(s(z0)))), a__dbl(a__sqr(s(mark(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(z0))) -> c3(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(a__sqr(mark(z0)))), A__SQR(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(mark(sqr(0))), a__dbl(a__sqr(0))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(mark(sqr(nil))), a__dbl(a__sqr(nil))), A__SQR(mark(sqr(nil)))) A__SQR(s(sqr(x0))) -> c3(A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(mark(add(x0, x1))), a__dbl(add(mark(x0), mark(x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, add(z0, z1)))), a__dbl(a__add(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, terms(z0)))), a__dbl(a__add(mark(x0), a__terms(mark(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, sqr(z0)))), a__dbl(a__add(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, dbl(z0)))), a__dbl(a__add(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, first(z0, z1)))), a__dbl(a__add(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, half(z0)))), a__dbl(a__add(mark(x0), a__half(mark(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(add(x0, cons(z0, z1)))), a__dbl(a__add(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, recip(z0)))), a__dbl(a__add(mark(x0), recip(mark(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(add(x0, s(z0)))), a__dbl(a__add(mark(x0), s(mark(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(mark(add(x0, 0))), a__dbl(a__add(mark(x0), 0))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(mark(add(x0, nil))), a__dbl(a__add(mark(x0), nil))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(add(z0, z1), x1))), a__dbl(a__add(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(terms(z0), x1))), a__dbl(a__add(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(sqr(z0), x1))), a__dbl(a__add(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(dbl(z0), x1))), a__dbl(a__add(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(first(z0, z1), x1))), a__dbl(a__add(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(half(z0), x1))), a__dbl(a__add(a__half(mark(z0)), mark(x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(add(cons(z0, z1), x1))), a__dbl(a__add(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(recip(z0), x1))), a__dbl(a__add(recip(mark(z0)), mark(x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(add(s(z0), x1))), a__dbl(a__add(s(mark(z0)), mark(x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(mark(add(0, x1))), a__dbl(a__add(0, mark(x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(mark(add(nil, x1))), a__dbl(a__add(nil, mark(x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(add(z0, z1))) -> c3(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__SQR(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(add(x0, x1))) -> c3(A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(mark(dbl(x0))), a__dbl(dbl(mark(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(dbl(z0)))), a__dbl(a__dbl(a__dbl(mark(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(terms(z0)))), a__dbl(a__dbl(a__terms(mark(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(sqr(z0)))), a__dbl(a__dbl(a__sqr(mark(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(add(z0, z1)))), a__dbl(a__dbl(a__add(mark(z0), mark(z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(first(z0, z1)))), a__dbl(a__dbl(a__first(mark(z0), mark(z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(half(z0)))), a__dbl(a__dbl(a__half(mark(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(dbl(cons(z0, z1)))), a__dbl(a__dbl(cons(mark(z0), z1)))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(recip(z0)))), a__dbl(a__dbl(recip(mark(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(mark(dbl(s(z0)))), a__dbl(a__dbl(s(mark(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(z0))) -> c3(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(a__dbl(mark(z0)))), A__SQR(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(mark(dbl(0))), a__dbl(a__dbl(0))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(mark(dbl(nil))), a__dbl(a__dbl(nil))), A__SQR(mark(dbl(nil)))) A__SQR(s(dbl(x0))) -> c3(A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(mark(first(x0, x1))), a__dbl(first(mark(x0), mark(x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, first(z0, z1)))), a__dbl(a__first(mark(x0), a__first(mark(z0), mark(z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, terms(z0)))), a__dbl(a__first(mark(x0), a__terms(mark(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, sqr(z0)))), a__dbl(a__first(mark(x0), a__sqr(mark(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, add(z0, z1)))), a__dbl(a__first(mark(x0), a__add(mark(z0), mark(z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, dbl(z0)))), a__dbl(a__first(mark(x0), a__dbl(mark(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, half(z0)))), a__dbl(a__first(mark(x0), a__half(mark(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(first(x0, cons(z0, z1)))), a__dbl(a__first(mark(x0), cons(mark(z0), z1)))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, recip(z0)))), a__dbl(a__first(mark(x0), recip(mark(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(mark(first(x0, s(z0)))), a__dbl(a__first(mark(x0), s(mark(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(mark(first(x0, 0))), a__dbl(a__first(mark(x0), 0))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(mark(first(x0, nil))), a__dbl(a__first(mark(x0), nil))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(first(z0, z1), x1))), a__dbl(a__first(a__first(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(terms(z0), x1))), a__dbl(a__first(a__terms(mark(z0)), mark(x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(sqr(z0), x1))), a__dbl(a__first(a__sqr(mark(z0)), mark(x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(add(z0, z1), x1))), a__dbl(a__first(a__add(mark(z0), mark(z1)), mark(x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(dbl(z0), x1))), a__dbl(a__first(a__dbl(mark(z0)), mark(x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(half(z0), x1))), a__dbl(a__first(a__half(mark(z0)), mark(x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(first(cons(z0, z1), x1))), a__dbl(a__first(cons(mark(z0), z1), mark(x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(recip(z0), x1))), a__dbl(a__first(recip(mark(z0)), mark(x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(first(s(z0), x1))), a__dbl(a__first(s(mark(z0)), mark(x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(mark(first(0, x1))), a__dbl(a__first(0, mark(x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(mark(first(nil, x1))), a__dbl(a__first(nil, mark(x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(first(z0, z1))) -> c3(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(first(x0, x1))) -> c3(A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(mark(half(x0))), a__dbl(half(mark(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(mark(half(half(z0)))), a__dbl(a__half(a__half(mark(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(mark(half(terms(z0)))), a__dbl(a__half(a__terms(mark(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(half(sqr(z0)))), a__dbl(a__half(a__sqr(mark(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(add(z0, z1)))), a__dbl(a__half(a__add(mark(z0), mark(z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(half(dbl(z0)))), a__dbl(a__half(a__dbl(mark(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(first(z0, z1)))), a__dbl(a__half(a__first(mark(z0), mark(z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(half(cons(z0, z1)))), a__dbl(a__half(cons(mark(z0), z1)))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(mark(half(recip(z0)))), a__dbl(a__half(recip(mark(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(mark(half(s(z0)))), a__dbl(a__half(s(mark(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(z0))) -> c3(A__ADD(a__sqr(a__half(mark(z0))), a__dbl(a__half(mark(z0)))), A__SQR(mark(half(z0))), MARK(half(z0))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(mark(half(0))), a__dbl(a__half(0))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(mark(half(nil))), a__dbl(a__half(nil))), A__SQR(mark(half(nil)))) A__SQR(s(half(x0))) -> c3(A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(cons(z0, z1), x1))), a__dbl(cons(cons(mark(z0), z1), x1))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(terms(z0), x1))), a__dbl(cons(a__terms(mark(z0)), x1))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(sqr(z0), x1))), a__dbl(cons(a__sqr(mark(z0)), x1))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(add(z0, z1), x1))), a__dbl(cons(a__add(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(dbl(z0), x1))), a__dbl(cons(a__dbl(mark(z0)), x1))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(mark(cons(first(z0, z1), x1))), a__dbl(cons(a__first(mark(z0), mark(z1)), x1))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(half(z0), x1))), a__dbl(cons(a__half(mark(z0)), x1))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(recip(z0), x1))), a__dbl(cons(recip(mark(z0)), x1))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(mark(cons(s(z0), x1))), a__dbl(cons(s(mark(z0)), x1))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(mark(cons(0, x1))), a__dbl(cons(0, x1))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(mark(cons(nil, x1))), a__dbl(cons(nil, x1))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(cons(mark(z0), z1))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(cons(x0, x1))) -> c3(A__SQR(mark(cons(x0, x1))), MARK(cons(x0, x1))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(mark(recip(recip(z0)))), a__dbl(recip(recip(mark(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(mark(recip(terms(z0)))), a__dbl(recip(a__terms(mark(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(recip(sqr(z0)))), a__dbl(recip(a__sqr(mark(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(add(z0, z1)))), a__dbl(recip(a__add(mark(z0), mark(z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(recip(dbl(z0)))), a__dbl(recip(a__dbl(mark(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(first(z0, z1)))), a__dbl(recip(a__first(mark(z0), mark(z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(mark(recip(half(z0)))), a__dbl(recip(a__half(mark(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(recip(cons(z0, z1)))), a__dbl(recip(cons(mark(z0), z1)))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(mark(recip(s(z0)))), a__dbl(recip(s(mark(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(mark(recip(0))), a__dbl(recip(0))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(mark(recip(nil))), a__dbl(recip(nil))), A__SQR(mark(recip(nil))), MARK(recip(nil))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(recip(mark(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(recip(x0))) -> c3(A__SQR(mark(recip(x0))), MARK(recip(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(mark(s(x0))), s(s(a__dbl(mark(mark(x0)))))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(mark(s(s(z0)))), a__dbl(s(s(mark(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(mark(s(terms(z0)))), a__dbl(s(a__terms(mark(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(mark(s(sqr(z0)))), a__dbl(s(a__sqr(mark(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(add(z0, z1)))), a__dbl(s(a__add(mark(z0), mark(z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(mark(s(dbl(z0)))), a__dbl(s(a__dbl(mark(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(first(z0, z1)))), a__dbl(s(a__first(mark(z0), mark(z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(mark(s(half(z0)))), a__dbl(s(a__half(mark(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(mark(s(cons(z0, z1)))), a__dbl(s(cons(mark(z0), z1)))), A__SQR(mark(s(cons(z0, z1)))), MARK(s(cons(z0, z1)))) A__SQR(s(s(recip(z0)))) -> c3(A__ADD(a__sqr(mark(s(recip(z0)))), a__dbl(s(recip(mark(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(mark(s(0))), a__dbl(s(0))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(mark(s(nil))), a__dbl(s(nil))), A__SQR(mark(s(nil))), MARK(s(nil))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(s(mark(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(s(x0))) -> c3(A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0))))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(x0))) -> c3(A__ADD(a__sqr(terms(mark(x0))), a__dbl(mark(terms(x0)))), A__SQR(mark(terms(x0))), MARK(terms(x0))) A__SQR(s(terms(terms(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__terms(mark(z0)))), a__dbl(mark(terms(terms(z0))))), A__SQR(mark(terms(terms(z0)))), MARK(terms(terms(z0)))) A__SQR(s(terms(sqr(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__sqr(mark(z0)))), a__dbl(mark(terms(sqr(z0))))), A__SQR(mark(terms(sqr(z0)))), MARK(terms(sqr(z0)))) A__SQR(s(terms(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__add(mark(z0), mark(z1)))), a__dbl(mark(terms(add(z0, z1))))), A__SQR(mark(terms(add(z0, z1)))), MARK(terms(add(z0, z1)))) A__SQR(s(terms(dbl(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__dbl(mark(z0)))), a__dbl(mark(terms(dbl(z0))))), A__SQR(mark(terms(dbl(z0)))), MARK(terms(dbl(z0)))) A__SQR(s(terms(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(a__first(mark(z0), mark(z1)))), a__dbl(mark(terms(first(z0, z1))))), A__SQR(mark(terms(first(z0, z1)))), MARK(terms(first(z0, z1)))) A__SQR(s(terms(half(z0)))) -> c3(A__ADD(a__sqr(a__terms(a__half(mark(z0)))), a__dbl(mark(terms(half(z0))))), A__SQR(mark(terms(half(z0)))), MARK(terms(half(z0)))) A__SQR(s(terms(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__terms(cons(mark(z0), z1))), a__dbl(mark(terms(cons(z0, z1))))), A__SQR(mark(terms(cons(z0, z1)))), MARK(terms(cons(z0, z1)))) A__SQR(s(terms(recip(z0)))) -> c3(A__ADD(a__sqr(a__terms(recip(mark(z0)))), a__dbl(mark(terms(recip(z0))))), A__SQR(mark(terms(recip(z0)))), MARK(terms(recip(z0)))) A__SQR(s(terms(s(z0)))) -> c3(A__ADD(a__sqr(a__terms(s(mark(z0)))), a__dbl(mark(terms(s(z0))))), A__SQR(mark(terms(s(z0)))), MARK(terms(s(z0)))) A__SQR(s(terms(0))) -> c3(A__ADD(a__sqr(a__terms(0)), a__dbl(mark(terms(0)))), A__SQR(mark(terms(0)))) A__SQR(s(terms(nil))) -> c3(A__ADD(a__sqr(a__terms(nil)), a__dbl(mark(terms(nil)))), A__SQR(mark(terms(nil)))) A__SQR(s(sqr(x0))) -> c3(A__ADD(a__sqr(sqr(mark(x0))), a__dbl(mark(sqr(x0)))), A__SQR(mark(sqr(x0))), MARK(sqr(x0))) A__SQR(s(sqr(terms(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__terms(mark(z0)))), a__dbl(mark(sqr(terms(z0))))), A__SQR(mark(sqr(terms(z0)))), MARK(sqr(terms(z0)))) A__SQR(s(sqr(sqr(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__sqr(mark(z0)))), a__dbl(mark(sqr(sqr(z0))))), A__SQR(mark(sqr(sqr(z0)))), MARK(sqr(sqr(z0)))) A__SQR(s(sqr(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__add(mark(z0), mark(z1)))), a__dbl(mark(sqr(add(z0, z1))))), A__SQR(mark(sqr(add(z0, z1)))), MARK(sqr(add(z0, z1)))) A__SQR(s(sqr(dbl(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__dbl(mark(z0)))), a__dbl(mark(sqr(dbl(z0))))), A__SQR(mark(sqr(dbl(z0)))), MARK(sqr(dbl(z0)))) A__SQR(s(sqr(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(a__first(mark(z0), mark(z1)))), a__dbl(mark(sqr(first(z0, z1))))), A__SQR(mark(sqr(first(z0, z1)))), MARK(sqr(first(z0, z1)))) A__SQR(s(sqr(half(z0)))) -> c3(A__ADD(a__sqr(a__sqr(a__half(mark(z0)))), a__dbl(mark(sqr(half(z0))))), A__SQR(mark(sqr(half(z0)))), MARK(sqr(half(z0)))) A__SQR(s(sqr(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__sqr(cons(mark(z0), z1))), a__dbl(mark(sqr(cons(z0, z1))))), A__SQR(mark(sqr(cons(z0, z1)))), MARK(sqr(cons(z0, z1)))) A__SQR(s(sqr(recip(z0)))) -> c3(A__ADD(a__sqr(a__sqr(recip(mark(z0)))), a__dbl(mark(sqr(recip(z0))))), A__SQR(mark(sqr(recip(z0)))), MARK(sqr(recip(z0)))) A__SQR(s(sqr(s(z0)))) -> c3(A__ADD(a__sqr(a__sqr(s(mark(z0)))), a__dbl(mark(sqr(s(z0))))), A__SQR(mark(sqr(s(z0)))), MARK(sqr(s(z0)))) A__SQR(s(sqr(0))) -> c3(A__ADD(a__sqr(a__sqr(0)), a__dbl(mark(sqr(0)))), A__SQR(mark(sqr(0)))) A__SQR(s(sqr(nil))) -> c3(A__ADD(a__sqr(a__sqr(nil)), a__dbl(mark(sqr(nil)))), A__SQR(mark(sqr(nil)))) A__SQR(s(add(x0, x1))) -> c3(A__ADD(a__sqr(add(mark(x0), mark(x1))), a__dbl(mark(add(x0, x1)))), A__SQR(mark(add(x0, x1))), MARK(add(x0, x1))) A__SQR(s(add(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__terms(mark(z0)))), a__dbl(mark(add(x0, terms(z0))))), A__SQR(mark(add(x0, terms(z0)))), MARK(add(x0, terms(z0)))) A__SQR(s(add(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(add(x0, sqr(z0))))), A__SQR(mark(add(x0, sqr(z0)))), MARK(add(x0, sqr(z0)))) A__SQR(s(add(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(add(x0, add(z0, z1))))), A__SQR(mark(add(x0, add(z0, z1)))), MARK(add(x0, add(z0, z1)))) A__SQR(s(add(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(add(x0, dbl(z0))))), A__SQR(mark(add(x0, dbl(z0)))), MARK(add(x0, dbl(z0)))) A__SQR(s(add(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(add(x0, first(z0, z1))))), A__SQR(mark(add(x0, first(z0, z1)))), MARK(add(x0, first(z0, z1)))) A__SQR(s(add(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), a__half(mark(z0)))), a__dbl(mark(add(x0, half(z0))))), A__SQR(mark(add(x0, half(z0)))), MARK(add(x0, half(z0)))) A__SQR(s(add(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), cons(mark(z0), z1))), a__dbl(mark(add(x0, cons(z0, z1))))), A__SQR(mark(add(x0, cons(z0, z1)))), MARK(add(x0, cons(z0, z1)))) A__SQR(s(add(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), recip(mark(z0)))), a__dbl(mark(add(x0, recip(z0))))), A__SQR(mark(add(x0, recip(z0)))), MARK(add(x0, recip(z0)))) A__SQR(s(add(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__add(mark(x0), s(mark(z0)))), a__dbl(mark(add(x0, s(z0))))), A__SQR(mark(add(x0, s(z0)))), MARK(add(x0, s(z0)))) A__SQR(s(add(x0, 0))) -> c3(A__ADD(a__sqr(a__add(mark(x0), 0)), a__dbl(mark(add(x0, 0)))), A__SQR(mark(add(x0, 0))), MARK(add(x0, 0))) A__SQR(s(add(x0, nil))) -> c3(A__ADD(a__sqr(a__add(mark(x0), nil)), a__dbl(mark(add(x0, nil)))), A__SQR(mark(add(x0, nil))), MARK(add(x0, nil))) A__SQR(s(add(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__terms(mark(z0)), mark(x1))), a__dbl(mark(add(terms(z0), x1)))), A__SQR(mark(add(terms(z0), x1))), MARK(add(terms(z0), x1))) A__SQR(s(add(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(add(sqr(z0), x1)))), A__SQR(mark(add(sqr(z0), x1))), MARK(add(sqr(z0), x1))) A__SQR(s(add(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(add(z0, z1), x1)))), A__SQR(mark(add(add(z0, z1), x1))), MARK(add(add(z0, z1), x1))) A__SQR(s(add(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(add(dbl(z0), x1)))), A__SQR(mark(add(dbl(z0), x1))), MARK(add(dbl(z0), x1))) A__SQR(s(add(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(add(first(z0, z1), x1)))), A__SQR(mark(add(first(z0, z1), x1))), MARK(add(first(z0, z1), x1))) A__SQR(s(add(half(z0), x1))) -> c3(A__ADD(a__sqr(a__add(a__half(mark(z0)), mark(x1))), a__dbl(mark(add(half(z0), x1)))), A__SQR(mark(add(half(z0), x1))), MARK(add(half(z0), x1))) A__SQR(s(add(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__add(cons(mark(z0), z1), mark(x1))), a__dbl(mark(add(cons(z0, z1), x1)))), A__SQR(mark(add(cons(z0, z1), x1))), MARK(add(cons(z0, z1), x1))) A__SQR(s(add(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__add(recip(mark(z0)), mark(x1))), a__dbl(mark(add(recip(z0), x1)))), A__SQR(mark(add(recip(z0), x1))), MARK(add(recip(z0), x1))) A__SQR(s(add(s(z0), x1))) -> c3(A__ADD(a__sqr(a__add(s(mark(z0)), mark(x1))), a__dbl(mark(add(s(z0), x1)))), A__SQR(mark(add(s(z0), x1))), MARK(add(s(z0), x1))) A__SQR(s(add(0, x1))) -> c3(A__ADD(a__sqr(a__add(0, mark(x1))), a__dbl(mark(add(0, x1)))), A__SQR(mark(add(0, x1))), MARK(add(0, x1))) A__SQR(s(add(nil, x1))) -> c3(A__ADD(a__sqr(a__add(nil, mark(x1))), a__dbl(mark(add(nil, x1)))), A__SQR(mark(add(nil, x1))), MARK(add(nil, x1))) A__SQR(s(dbl(x0))) -> c3(A__ADD(a__sqr(dbl(mark(x0))), a__dbl(mark(dbl(x0)))), A__SQR(mark(dbl(x0))), MARK(dbl(x0))) A__SQR(s(dbl(terms(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__terms(mark(z0)))), a__dbl(mark(dbl(terms(z0))))), A__SQR(mark(dbl(terms(z0)))), MARK(dbl(terms(z0)))) A__SQR(s(dbl(sqr(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__sqr(mark(z0)))), a__dbl(mark(dbl(sqr(z0))))), A__SQR(mark(dbl(sqr(z0)))), MARK(dbl(sqr(z0)))) A__SQR(s(dbl(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__add(mark(z0), mark(z1)))), a__dbl(mark(dbl(add(z0, z1))))), A__SQR(mark(dbl(add(z0, z1)))), MARK(dbl(add(z0, z1)))) A__SQR(s(dbl(dbl(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__dbl(mark(z0)))), a__dbl(mark(dbl(dbl(z0))))), A__SQR(mark(dbl(dbl(z0)))), MARK(dbl(dbl(z0)))) A__SQR(s(dbl(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(a__first(mark(z0), mark(z1)))), a__dbl(mark(dbl(first(z0, z1))))), A__SQR(mark(dbl(first(z0, z1)))), MARK(dbl(first(z0, z1)))) A__SQR(s(dbl(half(z0)))) -> c3(A__ADD(a__sqr(a__dbl(a__half(mark(z0)))), a__dbl(mark(dbl(half(z0))))), A__SQR(mark(dbl(half(z0)))), MARK(dbl(half(z0)))) A__SQR(s(dbl(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__dbl(cons(mark(z0), z1))), a__dbl(mark(dbl(cons(z0, z1))))), A__SQR(mark(dbl(cons(z0, z1)))), MARK(dbl(cons(z0, z1)))) A__SQR(s(dbl(recip(z0)))) -> c3(A__ADD(a__sqr(a__dbl(recip(mark(z0)))), a__dbl(mark(dbl(recip(z0))))), A__SQR(mark(dbl(recip(z0)))), MARK(dbl(recip(z0)))) A__SQR(s(dbl(s(z0)))) -> c3(A__ADD(a__sqr(a__dbl(s(mark(z0)))), a__dbl(mark(dbl(s(z0))))), A__SQR(mark(dbl(s(z0)))), MARK(dbl(s(z0)))) A__SQR(s(dbl(0))) -> c3(A__ADD(a__sqr(a__dbl(0)), a__dbl(mark(dbl(0)))), A__SQR(mark(dbl(0)))) A__SQR(s(dbl(nil))) -> c3(A__ADD(a__sqr(a__dbl(nil)), a__dbl(mark(dbl(nil)))), A__SQR(mark(dbl(nil)))) A__SQR(s(first(x0, x1))) -> c3(A__ADD(a__sqr(first(mark(x0), mark(x1))), a__dbl(mark(first(x0, x1)))), A__SQR(mark(first(x0, x1))), MARK(first(x0, x1))) A__SQR(s(first(x0, terms(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__terms(mark(z0)))), a__dbl(mark(first(x0, terms(z0))))), A__SQR(mark(first(x0, terms(z0)))), MARK(first(x0, terms(z0)))) A__SQR(s(first(x0, sqr(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__sqr(mark(z0)))), a__dbl(mark(first(x0, sqr(z0))))), A__SQR(mark(first(x0, sqr(z0)))), MARK(first(x0, sqr(z0)))) A__SQR(s(first(x0, add(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__add(mark(z0), mark(z1)))), a__dbl(mark(first(x0, add(z0, z1))))), A__SQR(mark(first(x0, add(z0, z1)))), MARK(first(x0, add(z0, z1)))) A__SQR(s(first(x0, dbl(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__dbl(mark(z0)))), a__dbl(mark(first(x0, dbl(z0))))), A__SQR(mark(first(x0, dbl(z0)))), MARK(first(x0, dbl(z0)))) A__SQR(s(first(x0, first(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__first(mark(z0), mark(z1)))), a__dbl(mark(first(x0, first(z0, z1))))), A__SQR(mark(first(x0, first(z0, z1)))), MARK(first(x0, first(z0, z1)))) A__SQR(s(first(x0, half(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), a__half(mark(z0)))), a__dbl(mark(first(x0, half(z0))))), A__SQR(mark(first(x0, half(z0)))), MARK(first(x0, half(z0)))) A__SQR(s(first(x0, cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), cons(mark(z0), z1))), a__dbl(mark(first(x0, cons(z0, z1))))), A__SQR(mark(first(x0, cons(z0, z1)))), MARK(first(x0, cons(z0, z1)))) A__SQR(s(first(x0, recip(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), recip(mark(z0)))), a__dbl(mark(first(x0, recip(z0))))), A__SQR(mark(first(x0, recip(z0)))), MARK(first(x0, recip(z0)))) A__SQR(s(first(x0, s(z0)))) -> c3(A__ADD(a__sqr(a__first(mark(x0), s(mark(z0)))), a__dbl(mark(first(x0, s(z0))))), A__SQR(mark(first(x0, s(z0)))), MARK(first(x0, s(z0)))) A__SQR(s(first(x0, 0))) -> c3(A__ADD(a__sqr(a__first(mark(x0), 0)), a__dbl(mark(first(x0, 0)))), A__SQR(mark(first(x0, 0))), MARK(first(x0, 0))) A__SQR(s(first(x0, nil))) -> c3(A__ADD(a__sqr(a__first(mark(x0), nil)), a__dbl(mark(first(x0, nil)))), A__SQR(mark(first(x0, nil))), MARK(first(x0, nil))) A__SQR(s(first(terms(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__terms(mark(z0)), mark(x1))), a__dbl(mark(first(terms(z0), x1)))), A__SQR(mark(first(terms(z0), x1))), MARK(first(terms(z0), x1))) A__SQR(s(first(sqr(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__sqr(mark(z0)), mark(x1))), a__dbl(mark(first(sqr(z0), x1)))), A__SQR(mark(first(sqr(z0), x1))), MARK(first(sqr(z0), x1))) A__SQR(s(first(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__add(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(add(z0, z1), x1)))), A__SQR(mark(first(add(z0, z1), x1))), MARK(first(add(z0, z1), x1))) A__SQR(s(first(dbl(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__dbl(mark(z0)), mark(x1))), a__dbl(mark(first(dbl(z0), x1)))), A__SQR(mark(first(dbl(z0), x1))), MARK(first(dbl(z0), x1))) A__SQR(s(first(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(a__first(mark(z0), mark(z1)), mark(x1))), a__dbl(mark(first(first(z0, z1), x1)))), A__SQR(mark(first(first(z0, z1), x1))), MARK(first(first(z0, z1), x1))) A__SQR(s(first(half(z0), x1))) -> c3(A__ADD(a__sqr(a__first(a__half(mark(z0)), mark(x1))), a__dbl(mark(first(half(z0), x1)))), A__SQR(mark(first(half(z0), x1))), MARK(first(half(z0), x1))) A__SQR(s(first(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(a__first(cons(mark(z0), z1), mark(x1))), a__dbl(mark(first(cons(z0, z1), x1)))), A__SQR(mark(first(cons(z0, z1), x1))), MARK(first(cons(z0, z1), x1))) A__SQR(s(first(recip(z0), x1))) -> c3(A__ADD(a__sqr(a__first(recip(mark(z0)), mark(x1))), a__dbl(mark(first(recip(z0), x1)))), A__SQR(mark(first(recip(z0), x1))), MARK(first(recip(z0), x1))) A__SQR(s(first(s(z0), x1))) -> c3(A__ADD(a__sqr(a__first(s(mark(z0)), mark(x1))), a__dbl(mark(first(s(z0), x1)))), A__SQR(mark(first(s(z0), x1))), MARK(first(s(z0), x1))) A__SQR(s(first(0, x1))) -> c3(A__ADD(a__sqr(a__first(0, mark(x1))), a__dbl(mark(first(0, x1)))), A__SQR(mark(first(0, x1))), MARK(first(0, x1))) A__SQR(s(first(nil, x1))) -> c3(A__ADD(a__sqr(a__first(nil, mark(x1))), a__dbl(mark(first(nil, x1)))), A__SQR(mark(first(nil, x1))), MARK(first(nil, x1))) A__SQR(s(half(x0))) -> c3(A__ADD(a__sqr(half(mark(x0))), a__dbl(mark(half(x0)))), A__SQR(mark(half(x0))), MARK(half(x0))) A__SQR(s(half(terms(z0)))) -> c3(A__ADD(a__sqr(a__half(a__terms(mark(z0)))), a__dbl(mark(half(terms(z0))))), A__SQR(mark(half(terms(z0)))), MARK(half(terms(z0)))) A__SQR(s(half(sqr(z0)))) -> c3(A__ADD(a__sqr(a__half(a__sqr(mark(z0)))), a__dbl(mark(half(sqr(z0))))), A__SQR(mark(half(sqr(z0)))), MARK(half(sqr(z0)))) A__SQR(s(half(add(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__add(mark(z0), mark(z1)))), a__dbl(mark(half(add(z0, z1))))), A__SQR(mark(half(add(z0, z1)))), MARK(half(add(z0, z1)))) A__SQR(s(half(dbl(z0)))) -> c3(A__ADD(a__sqr(a__half(a__dbl(mark(z0)))), a__dbl(mark(half(dbl(z0))))), A__SQR(mark(half(dbl(z0)))), MARK(half(dbl(z0)))) A__SQR(s(half(first(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(a__first(mark(z0), mark(z1)))), a__dbl(mark(half(first(z0, z1))))), A__SQR(mark(half(first(z0, z1)))), MARK(half(first(z0, z1)))) A__SQR(s(half(half(z0)))) -> c3(A__ADD(a__sqr(a__half(a__half(mark(z0)))), a__dbl(mark(half(half(z0))))), A__SQR(mark(half(half(z0)))), MARK(half(half(z0)))) A__SQR(s(half(cons(z0, z1)))) -> c3(A__ADD(a__sqr(a__half(cons(mark(z0), z1))), a__dbl(mark(half(cons(z0, z1))))), A__SQR(mark(half(cons(z0, z1)))), MARK(half(cons(z0, z1)))) A__SQR(s(half(recip(z0)))) -> c3(A__ADD(a__sqr(a__half(recip(mark(z0)))), a__dbl(mark(half(recip(z0))))), A__SQR(mark(half(recip(z0)))), MARK(half(recip(z0)))) A__SQR(s(half(s(z0)))) -> c3(A__ADD(a__sqr(a__half(s(mark(z0)))), a__dbl(mark(half(s(z0))))), A__SQR(mark(half(s(z0)))), MARK(half(s(z0)))) A__SQR(s(half(0))) -> c3(A__ADD(a__sqr(a__half(0)), a__dbl(mark(half(0)))), A__SQR(mark(half(0)))) A__SQR(s(half(nil))) -> c3(A__ADD(a__sqr(a__half(nil)), a__dbl(mark(half(nil)))), A__SQR(mark(half(nil)))) A__SQR(s(cons(terms(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__terms(mark(z0)), x1)), a__dbl(mark(cons(terms(z0), x1)))), A__SQR(mark(cons(terms(z0), x1))), MARK(cons(terms(z0), x1))) A__SQR(s(cons(sqr(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__sqr(mark(z0)), x1)), a__dbl(mark(cons(sqr(z0), x1)))), A__SQR(mark(cons(sqr(z0), x1))), MARK(cons(sqr(z0), x1))) A__SQR(s(cons(add(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(a__add(mark(z0), mark(z1)), x1)), a__dbl(mark(cons(add(z0, z1), x1)))), A__SQR(mark(cons(add(z0, z1), x1))), MARK(cons(add(z0, z1), x1))) A__SQR(s(cons(dbl(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__dbl(mark(z0)), x1)), a__dbl(mark(cons(dbl(z0), x1)))), A__SQR(mark(cons(dbl(z0), x1))), MARK(cons(dbl(z0), x1))) A__SQR(s(cons(first(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(a__first(mark(z0), mark(z1)), x1)), a__dbl(mark(cons(first(z0, z1), x1)))), A__SQR(mark(cons(first(z0, z1), x1))), MARK(cons(first(z0, z1), x1))) A__SQR(s(cons(half(z0), x1))) -> c3(A__ADD(a__sqr(cons(a__half(mark(z0)), x1)), a__dbl(mark(cons(half(z0), x1)))), A__SQR(mark(cons(half(z0), x1))), MARK(cons(half(z0), x1))) A__SQR(s(cons(cons(z0, z1), x1))) -> c3(A__ADD(a__sqr(cons(cons(mark(z0), z1), x1)), a__dbl(mark(cons(cons(z0, z1), x1)))), A__SQR(mark(cons(cons(z0, z1), x1))), MARK(cons(cons(z0, z1), x1))) A__SQR(s(cons(recip(z0), x1))) -> c3(A__ADD(a__sqr(cons(recip(mark(z0)), x1)), a__dbl(mark(cons(recip(z0), x1)))), A__SQR(mark(cons(recip(z0), x1))), MARK(cons(recip(z0), x1))) A__SQR(s(cons(s(z0), x1))) -> c3(A__ADD(a__sqr(cons(s(mark(z0)), x1)), a__dbl(mark(cons(s(z0), x1)))), A__SQR(mark(cons(s(z0), x1))), MARK(cons(s(z0), x1))) A__SQR(s(cons(0, x1))) -> c3(A__ADD(a__sqr(cons(0, x1)), a__dbl(mark(cons(0, x1)))), A__SQR(mark(cons(0, x1))), MARK(cons(0, x1))) A__SQR(s(cons(nil, x1))) -> c3(A__ADD(a__sqr(cons(nil, x1)), a__dbl(mark(cons(nil, x1)))), A__SQR(mark(cons(nil, x1))), MARK(cons(nil, x1))) A__SQR(s(recip(terms(z0)))) -> c3(A__ADD(a__sqr(recip(a__terms(mark(z0)))), a__dbl(mark(recip(terms(z0))))), A__SQR(mark(recip(terms(z0)))), MARK(recip(terms(z0)))) A__SQR(s(recip(sqr(z0)))) -> c3(A__ADD(a__sqr(recip(a__sqr(mark(z0)))), a__dbl(mark(recip(sqr(z0))))), A__SQR(mark(recip(sqr(z0)))), MARK(recip(sqr(z0)))) A__SQR(s(recip(add(z0, z1)))) -> c3(A__ADD(a__sqr(recip(a__add(mark(z0), mark(z1)))), a__dbl(mark(recip(add(z0, z1))))), A__SQR(mark(recip(add(z0, z1)))), MARK(recip(add(z0, z1)))) A__SQR(s(recip(dbl(z0)))) -> c3(A__ADD(a__sqr(recip(a__dbl(mark(z0)))), a__dbl(mark(recip(dbl(z0))))), A__SQR(mark(recip(dbl(z0)))), MARK(recip(dbl(z0)))) A__SQR(s(recip(first(z0, z1)))) -> c3(A__ADD(a__sqr(recip(a__first(mark(z0), mark(z1)))), a__dbl(mark(recip(first(z0, z1))))), A__SQR(mark(recip(first(z0, z1)))), MARK(recip(first(z0, z1)))) A__SQR(s(recip(half(z0)))) -> c3(A__ADD(a__sqr(recip(a__half(mark(z0)))), a__dbl(mark(recip(half(z0))))), A__SQR(mark(recip(half(z0)))), MARK(recip(half(z0)))) A__SQR(s(recip(cons(z0, z1)))) -> c3(A__ADD(a__sqr(recip(cons(mark(z0), z1))), a__dbl(mark(recip(cons(z0, z1))))), A__SQR(mark(recip(cons(z0, z1)))), MARK(recip(cons(z0, z1)))) A__SQR(s(recip(recip(z0)))) -> c3(A__ADD(a__sqr(recip(recip(mark(z0)))), a__dbl(mark(recip(recip(z0))))), A__SQR(mark(recip(recip(z0)))), MARK(recip(recip(z0)))) A__SQR(s(recip(s(z0)))) -> c3(A__ADD(a__sqr(recip(s(mark(z0)))), a__dbl(mark(recip(s(z0))))), A__SQR(mark(recip(s(z0)))), MARK(recip(s(z0)))) A__SQR(s(recip(0))) -> c3(A__ADD(a__sqr(recip(0)), a__dbl(mark(recip(0)))), A__SQR(mark(recip(0))), MARK(recip(0))) A__SQR(s(recip(nil))) -> c3(A__ADD(a__sqr(recip(nil)), a__dbl(mark(recip(nil)))), A__SQR(mark(recip(nil))), MARK(recip(nil))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, a__half_1, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, A__HALF_1, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_1, c29_1, c30_1, c31_1, c_2, c_1, c3_3, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c18_2, c18_1, c21_2, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (245) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (246) 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(a__add(a__sqr(mark(X)), a__dbl(mark(X)))) [1] a__dbl(0) -> 0 [1] a__dbl(s(X)) -> s(s(a__dbl(mark(X)))) [1] a__add(0, X) -> mark(X) [1] a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) [1] a__first(0, X) -> nil [1] a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1] a__half(0) -> 0 [1] a__half(s(0)) -> 0 [1] a__half(s(s(X))) -> s(a__half(mark(X))) [1] a__half(dbl(X)) -> mark(X) [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(half(X)) -> a__half(mark(X)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(recip(X)) -> recip(mark(X)) [1] mark(s(X)) -> s(mark(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] a__half(X) -> half(X) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (247) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (248) 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(a__add(a__sqr(mark(X)), a__dbl(mark(X)))) [1] a__dbl(0) -> 0 [1] a__dbl(s(X)) -> s(s(a__dbl(mark(X)))) [1] a__add(0, X) -> mark(X) [1] a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) [1] a__first(0, X) -> nil [1] a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1] a__half(0) -> 0 [1] a__half(s(0)) -> 0 [1] a__half(s(s(X))) -> s(a__half(mark(X))) [1] a__half(dbl(X)) -> mark(X) [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(half(X)) -> a__half(mark(X)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(recip(X)) -> recip(mark(X)) [1] mark(s(X)) -> s(mark(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] a__half(X) -> half(X) [1] The TRS has the following type information: a__terms :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half cons :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half recip :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half a__sqr :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half mark :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half terms :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half s :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half 0 :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half a__add :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half a__dbl :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half a__first :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half nil :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half first :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half a__half :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half dbl :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half sqr :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half add :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half half :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half Rewrite Strategy: INNERMOST ---------------------------------------- (249) 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__dbl_1 a__terms_1 a__first_2 a__half_1 a__add_2 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (250) 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(a__add(a__sqr(mark(X)), a__dbl(mark(X)))) [1] a__dbl(0) -> 0 [1] a__dbl(s(X)) -> s(s(a__dbl(mark(X)))) [1] a__add(0, X) -> mark(X) [1] a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) [1] a__first(0, X) -> nil [1] a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1] a__half(0) -> 0 [1] a__half(s(0)) -> 0 [1] a__half(s(s(X))) -> s(a__half(mark(X))) [1] a__half(dbl(X)) -> mark(X) [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(half(X)) -> a__half(mark(X)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(recip(X)) -> recip(mark(X)) [1] mark(s(X)) -> s(mark(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] a__half(X) -> half(X) [1] The TRS has the following type information: a__terms :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half cons :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half recip :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half a__sqr :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half mark :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half terms :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half s :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half 0 :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half a__add :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half a__dbl :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half a__first :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half nil :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half first :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half a__half :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half dbl :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half sqr :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half add :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half half :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half Rewrite Strategy: INNERMOST ---------------------------------------- (251) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (252) 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(half(X4)) -> cons(recip(a__sqr(a__half(mark(X4)))), terms(s(half(X4)))) [2] a__terms(cons(X11, X21)) -> cons(recip(a__sqr(cons(mark(X11), X21))), terms(s(cons(X11, X21)))) [2] a__terms(recip(X5)) -> cons(recip(a__sqr(recip(mark(X5)))), terms(s(recip(X5)))) [2] a__terms(s(X6)) -> cons(recip(a__sqr(s(mark(X6)))), terms(s(s(X6)))) [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(terms(X7))) -> s(a__add(a__sqr(a__terms(mark(X7))), a__dbl(a__terms(mark(X7))))) [3] a__sqr(s(sqr(X8))) -> s(a__add(a__sqr(a__sqr(mark(X8))), a__dbl(a__sqr(mark(X8))))) [3] a__sqr(s(add(X12, X22))) -> s(a__add(a__sqr(a__add(mark(X12), mark(X22))), a__dbl(a__add(mark(X12), mark(X22))))) [3] a__sqr(s(dbl(X9))) -> s(a__add(a__sqr(a__dbl(mark(X9))), a__dbl(a__dbl(mark(X9))))) [3] a__sqr(s(first(X13, X23))) -> s(a__add(a__sqr(a__first(mark(X13), mark(X23))), a__dbl(a__first(mark(X13), mark(X23))))) [3] a__sqr(s(half(X10))) -> s(a__add(a__sqr(a__half(mark(X10))), a__dbl(a__half(mark(X10))))) [3] a__sqr(s(cons(X14, X24))) -> s(a__add(a__sqr(cons(mark(X14), X24)), a__dbl(cons(mark(X14), X24)))) [3] a__sqr(s(recip(X15))) -> s(a__add(a__sqr(recip(mark(X15))), a__dbl(recip(mark(X15))))) [3] a__sqr(s(s(X16))) -> s(a__add(a__sqr(s(mark(X16))), a__dbl(s(mark(X16))))) [3] a__sqr(s(0)) -> s(a__add(a__sqr(0), a__dbl(0))) [3] a__sqr(s(nil)) -> s(a__add(a__sqr(nil), a__dbl(nil))) [3] a__dbl(0) -> 0 [1] a__dbl(s(terms(X17))) -> s(s(a__dbl(a__terms(mark(X17))))) [2] a__dbl(s(sqr(X18))) -> s(s(a__dbl(a__sqr(mark(X18))))) [2] a__dbl(s(add(X19, X25))) -> s(s(a__dbl(a__add(mark(X19), mark(X25))))) [2] a__dbl(s(dbl(X20))) -> s(s(a__dbl(a__dbl(mark(X20))))) [2] a__dbl(s(first(X110, X26))) -> s(s(a__dbl(a__first(mark(X110), mark(X26))))) [2] a__dbl(s(half(X27))) -> s(s(a__dbl(a__half(mark(X27))))) [2] a__dbl(s(cons(X111, X28))) -> s(s(a__dbl(cons(mark(X111), X28)))) [2] a__dbl(s(recip(X29))) -> s(s(a__dbl(recip(mark(X29))))) [2] a__dbl(s(s(X30))) -> s(s(a__dbl(s(mark(X30))))) [2] a__dbl(s(0)) -> s(s(a__dbl(0))) [2] a__dbl(s(nil)) -> s(s(a__dbl(nil))) [2] a__add(0, X) -> mark(X) [1] a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) [1] a__first(0, X) -> nil [1] a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1] a__half(0) -> 0 [1] a__half(s(0)) -> 0 [1] a__half(s(s(terms(X103)))) -> s(a__half(a__terms(mark(X103)))) [2] a__half(s(s(sqr(X104)))) -> s(a__half(a__sqr(mark(X104)))) [2] a__half(s(s(add(X148, X246)))) -> s(a__half(a__add(mark(X148), mark(X246)))) [2] a__half(s(s(dbl(X105)))) -> s(a__half(a__dbl(mark(X105)))) [2] a__half(s(s(first(X149, X247)))) -> s(a__half(a__first(mark(X149), mark(X247)))) [2] a__half(s(s(half(X106)))) -> s(a__half(a__half(mark(X106)))) [2] a__half(s(s(cons(X150, X248)))) -> s(a__half(cons(mark(X150), X248))) [2] a__half(s(s(recip(X107)))) -> s(a__half(recip(mark(X107)))) [2] a__half(s(s(s(X108)))) -> s(a__half(s(mark(X108)))) [2] a__half(s(s(0))) -> s(a__half(0)) [2] a__half(s(s(nil))) -> s(a__half(nil)) [2] a__half(dbl(X)) -> mark(X) [1] mark(terms(terms(X109))) -> a__terms(a__terms(mark(X109))) [2] mark(terms(sqr(X151))) -> a__terms(a__sqr(mark(X151))) [2] mark(terms(add(X152, X249))) -> a__terms(a__add(mark(X152), mark(X249))) [2] mark(terms(dbl(X153))) -> a__terms(a__dbl(mark(X153))) [2] mark(terms(first(X154, X250))) -> a__terms(a__first(mark(X154), mark(X250))) [2] mark(terms(half(X155))) -> a__terms(a__half(mark(X155))) [2] mark(terms(cons(X156, X251))) -> a__terms(cons(mark(X156), X251)) [2] mark(terms(recip(X157))) -> a__terms(recip(mark(X157))) [2] mark(terms(s(X158))) -> a__terms(s(mark(X158))) [2] mark(terms(0)) -> a__terms(0) [2] mark(terms(nil)) -> a__terms(nil) [2] mark(sqr(terms(X159))) -> a__sqr(a__terms(mark(X159))) [2] mark(sqr(sqr(X160))) -> a__sqr(a__sqr(mark(X160))) [2] mark(sqr(add(X161, X252))) -> a__sqr(a__add(mark(X161), mark(X252))) [2] mark(sqr(dbl(X162))) -> a__sqr(a__dbl(mark(X162))) [2] mark(sqr(first(X163, X253))) -> a__sqr(a__first(mark(X163), mark(X253))) [2] mark(sqr(half(X164))) -> a__sqr(a__half(mark(X164))) [2] mark(sqr(cons(X165, X254))) -> a__sqr(cons(mark(X165), X254)) [2] mark(sqr(recip(X166))) -> a__sqr(recip(mark(X166))) [2] mark(sqr(s(X167))) -> a__sqr(s(mark(X167))) [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(X321))) -> a__dbl(a__terms(mark(X321))) [2] mark(dbl(sqr(X322))) -> a__dbl(a__sqr(mark(X322))) [2] mark(dbl(add(X1125, X2111))) -> a__dbl(a__add(mark(X1125), mark(X2111))) [2] mark(dbl(dbl(X323))) -> a__dbl(a__dbl(mark(X323))) [2] mark(dbl(first(X1126, X2112))) -> a__dbl(a__first(mark(X1126), mark(X2112))) [2] mark(dbl(half(X324))) -> a__dbl(a__half(mark(X324))) [2] mark(dbl(cons(X1127, X2113))) -> a__dbl(cons(mark(X1127), X2113)) [2] mark(dbl(recip(X325))) -> a__dbl(recip(mark(X325))) [2] mark(dbl(s(X326))) -> a__dbl(s(mark(X326))) [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(half(terms(X399))) -> a__half(a__terms(mark(X399))) [2] mark(half(sqr(X400))) -> a__half(a__sqr(mark(X400))) [2] mark(half(add(X1164, X2150))) -> a__half(a__add(mark(X1164), mark(X2150))) [2] mark(half(dbl(X401))) -> a__half(a__dbl(mark(X401))) [2] mark(half(first(X1165, X2151))) -> a__half(a__first(mark(X1165), mark(X2151))) [2] mark(half(half(X402))) -> a__half(a__half(mark(X402))) [2] mark(half(cons(X1166, X2152))) -> a__half(cons(mark(X1166), X2152)) [2] mark(half(recip(X403))) -> a__half(recip(mark(X403))) [2] mark(half(s(X404))) -> a__half(s(mark(X404))) [2] mark(half(0)) -> a__half(0) [2] mark(half(nil)) -> a__half(nil) [2] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(recip(X)) -> recip(mark(X)) [1] mark(s(X)) -> s(mark(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] a__half(X) -> half(X) [1] The TRS has the following type information: a__terms :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half cons :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half recip :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half a__sqr :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half mark :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half terms :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half s :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half 0 :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half a__add :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half a__dbl :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half a__first :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half nil :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half first :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half a__half :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half dbl :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half sqr :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half add :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half half :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half Rewrite Strategy: INNERMOST ---------------------------------------- (253) 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 ---------------------------------------- (254) Obligation: Complexity RNTS consisting of the following rules: a__add(z, z') -{ 1 }-> mark(X) :|: z' = X, X >= 0, z = 0 a__add(z, z') -{ 1 }-> 1 + a__add(mark(X), mark(Y)) :|: z = 1 + X, z' = Y, Y >= 0, X >= 0 a__add(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__dbl(z) -{ 1 }-> 0 :|: z = 0 a__dbl(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(a__terms(mark(X17)))) :|: X17 >= 0, z = 1 + (1 + X17) a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(a__sqr(mark(X18)))) :|: X18 >= 0, z = 1 + (1 + X18) a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(a__half(mark(X27)))) :|: X27 >= 0, z = 1 + (1 + X27) a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(a__first(mark(X110), mark(X26)))) :|: X110 >= 0, X26 >= 0, z = 1 + (1 + X110 + X26) a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(a__dbl(mark(X20)))) :|: z = 1 + (1 + X20), X20 >= 0 a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(a__add(mark(X19), mark(X25)))) :|: z = 1 + (1 + X19 + X25), X19 >= 0, X25 >= 0 a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(1)) :|: z = 1 + 1 a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(0)) :|: z = 1 + 0 a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(1 + mark(X29))) :|: X29 >= 0, z = 1 + (1 + X29) a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(1 + mark(X30))) :|: z = 1 + (1 + X30), X30 >= 0 a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(1 + mark(X111) + X28)) :|: X28 >= 0, z = 1 + (1 + X111 + X28), X111 >= 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__half(z) -{ 1 }-> mark(X) :|: z = 1 + X, X >= 0 a__half(z) -{ 1 }-> 0 :|: z = 0 a__half(z) -{ 1 }-> 0 :|: z = 1 + 0 a__half(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__half(z) -{ 2 }-> 1 + a__half(a__terms(mark(X103))) :|: z = 1 + (1 + (1 + X103)), X103 >= 0 a__half(z) -{ 2 }-> 1 + a__half(a__sqr(mark(X104))) :|: X104 >= 0, z = 1 + (1 + (1 + X104)) a__half(z) -{ 2 }-> 1 + a__half(a__half(mark(X106))) :|: X106 >= 0, z = 1 + (1 + (1 + X106)) a__half(z) -{ 2 }-> 1 + a__half(a__first(mark(X149), mark(X247))) :|: X149 >= 0, X247 >= 0, z = 1 + (1 + (1 + X149 + X247)) a__half(z) -{ 2 }-> 1 + a__half(a__dbl(mark(X105))) :|: z = 1 + (1 + (1 + X105)), X105 >= 0 a__half(z) -{ 2 }-> 1 + a__half(a__add(mark(X148), mark(X246))) :|: X246 >= 0, X148 >= 0, z = 1 + (1 + (1 + X148 + X246)) a__half(z) -{ 2 }-> 1 + a__half(1) :|: z = 1 + (1 + 1) a__half(z) -{ 2 }-> 1 + a__half(0) :|: z = 1 + (1 + 0) a__half(z) -{ 2 }-> 1 + a__half(1 + mark(X107)) :|: X107 >= 0, z = 1 + (1 + (1 + X107)) a__half(z) -{ 2 }-> 1 + a__half(1 + mark(X108)) :|: z = 1 + (1 + (1 + X108)), X108 >= 0 a__half(z) -{ 2 }-> 1 + a__half(1 + mark(X150) + X248) :|: X248 >= 0, X150 >= 0, z = 1 + (1 + (1 + X150 + X248)) a__sqr(z) -{ 1 }-> 0 :|: z = 0 a__sqr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(a__terms(mark(X7))), a__dbl(a__terms(mark(X7)))) :|: X7 >= 0, z = 1 + (1 + X7) a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(a__sqr(mark(X8))), a__dbl(a__sqr(mark(X8)))) :|: X8 >= 0, z = 1 + (1 + X8) a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(a__half(mark(X10))), a__dbl(a__half(mark(X10)))) :|: z = 1 + (1 + X10), X10 >= 0 a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(a__first(mark(X13), mark(X23))), a__dbl(a__first(mark(X13), mark(X23)))) :|: z = 1 + (1 + X13 + X23), X13 >= 0, X23 >= 0 a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(a__dbl(mark(X9))), a__dbl(a__dbl(mark(X9)))) :|: X9 >= 0, z = 1 + (1 + X9) a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(a__add(mark(X12), mark(X22))), a__dbl(a__add(mark(X12), mark(X22)))) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(1), a__dbl(1)) :|: z = 1 + 1 a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(0), a__dbl(0)) :|: z = 1 + 0 a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(1 + mark(X15)), a__dbl(1 + mark(X15))) :|: z = 1 + (1 + X15), X15 >= 0 a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(1 + mark(X16)), a__dbl(1 + mark(X16))) :|: X16 >= 0, z = 1 + (1 + X16) a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(1 + mark(X14) + X24), a__dbl(1 + mark(X14) + X24)) :|: z = 1 + (1 + X14 + X24), X14 >= 0, X24 >= 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__half(mark(X4)))) + (1 + (1 + (1 + X4))) :|: z = 1 + X4, X4 >= 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 + mark(X5))) + (1 + (1 + (1 + X5))) :|: X5 >= 0, z = 1 + X5 a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(1 + mark(X6))) + (1 + (1 + (1 + X6))) :|: X6 >= 0, z = 1 + X6 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(X109))) :|: z = 1 + (1 + X109), X109 >= 0 mark(z) -{ 2 }-> a__terms(a__sqr(mark(X151))) :|: z = 1 + (1 + X151), X151 >= 0 mark(z) -{ 2 }-> a__terms(a__half(mark(X155))) :|: z = 1 + (1 + X155), X155 >= 0 mark(z) -{ 2 }-> a__terms(a__first(mark(X154), mark(X250))) :|: X154 >= 0, z = 1 + (1 + X154 + X250), X250 >= 0 mark(z) -{ 2 }-> a__terms(a__dbl(mark(X153))) :|: X153 >= 0, z = 1 + (1 + X153) mark(z) -{ 2 }-> a__terms(a__add(mark(X152), mark(X249))) :|: z = 1 + (1 + X152 + X249), X152 >= 0, X249 >= 0 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(X157)) :|: z = 1 + (1 + X157), X157 >= 0 mark(z) -{ 2 }-> a__terms(1 + mark(X158)) :|: X158 >= 0, z = 1 + (1 + X158) mark(z) -{ 2 }-> a__terms(1 + mark(X156) + X251) :|: X156 >= 0, X251 >= 0, z = 1 + (1 + X156 + X251) mark(z) -{ 2 }-> a__sqr(a__terms(mark(X159))) :|: z = 1 + (1 + X159), X159 >= 0 mark(z) -{ 2 }-> a__sqr(a__sqr(mark(X160))) :|: z = 1 + (1 + X160), X160 >= 0 mark(z) -{ 2 }-> a__sqr(a__half(mark(X164))) :|: X164 >= 0, z = 1 + (1 + X164) mark(z) -{ 2 }-> a__sqr(a__first(mark(X163), mark(X253))) :|: X163 >= 0, X253 >= 0, z = 1 + (1 + X163 + X253) mark(z) -{ 2 }-> a__sqr(a__dbl(mark(X162))) :|: X162 >= 0, z = 1 + (1 + X162) mark(z) -{ 2 }-> a__sqr(a__add(mark(X161), mark(X252))) :|: X252 >= 0, z = 1 + (1 + X161 + X252), X161 >= 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 + mark(X166)) :|: X166 >= 0, z = 1 + (1 + X166) mark(z) -{ 2 }-> a__sqr(1 + mark(X167)) :|: z = 1 + (1 + X167), X167 >= 0 mark(z) -{ 2 }-> a__sqr(1 + mark(X165) + X254) :|: X165 >= 0, z = 1 + (1 + X165 + X254), X254 >= 0 mark(z) -{ 2 }-> a__half(a__terms(mark(X399))) :|: X399 >= 0, z = 1 + (1 + X399) mark(z) -{ 2 }-> a__half(a__sqr(mark(X400))) :|: X400 >= 0, z = 1 + (1 + X400) mark(z) -{ 2 }-> a__half(a__half(mark(X402))) :|: z = 1 + (1 + X402), X402 >= 0 mark(z) -{ 2 }-> a__half(a__first(mark(X1165), mark(X2151))) :|: z = 1 + (1 + X1165 + X2151), X2151 >= 0, X1165 >= 0 mark(z) -{ 2 }-> a__half(a__dbl(mark(X401))) :|: z = 1 + (1 + X401), X401 >= 0 mark(z) -{ 2 }-> a__half(a__add(mark(X1164), mark(X2150))) :|: X1164 >= 0, X2150 >= 0, z = 1 + (1 + X1164 + X2150) mark(z) -{ 2 }-> a__half(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__half(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__half(1 + mark(X403)) :|: z = 1 + (1 + X403), X403 >= 0 mark(z) -{ 2 }-> a__half(1 + mark(X404)) :|: z = 1 + (1 + X404), X404 >= 0 mark(z) -{ 2 }-> a__half(1 + mark(X1166) + X2152) :|: X2152 >= 0, X1166 >= 0, z = 1 + (1 + X1166 + X2152) 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(X321))) :|: z = 1 + (1 + X321), X321 >= 0 mark(z) -{ 2 }-> a__dbl(a__sqr(mark(X322))) :|: z = 1 + (1 + X322), X322 >= 0 mark(z) -{ 2 }-> a__dbl(a__half(mark(X324))) :|: z = 1 + (1 + X324), X324 >= 0 mark(z) -{ 2 }-> a__dbl(a__first(mark(X1126), mark(X2112))) :|: z = 1 + (1 + X1126 + X2112), X2112 >= 0, X1126 >= 0 mark(z) -{ 2 }-> a__dbl(a__dbl(mark(X323))) :|: X323 >= 0, z = 1 + (1 + X323) mark(z) -{ 2 }-> a__dbl(a__add(mark(X1125), mark(X2111))) :|: X1125 >= 0, X2111 >= 0, z = 1 + (1 + X1125 + X2111) mark(z) -{ 2 }-> a__dbl(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__dbl(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__dbl(1 + mark(X325)) :|: X325 >= 0, z = 1 + (1 + X325) mark(z) -{ 2 }-> a__dbl(1 + mark(X326)) :|: X326 >= 0, z = 1 + (1 + X326) mark(z) -{ 2 }-> a__dbl(1 + mark(X1127) + X2113) :|: X2113 >= 0, X1127 >= 0, z = 1 + (1 + X1127 + X2113) 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 + mark(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 ---------------------------------------- (255) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (256) Obligation: Complexity RNTS consisting of the following rules: a__add(z, z') -{ 1 }-> mark(z') :|: z' >= 0, z = 0 a__add(z, z') -{ 1 }-> 1 + a__add(mark(z - 1), mark(z')) :|: z' >= 0, z - 1 >= 0 a__add(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__dbl(z) -{ 1 }-> 0 :|: z = 0 a__dbl(z) -{ 1 }-> 1 + z :|: z >= 0 a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(a__terms(mark(z - 2)))) :|: z - 2 >= 0 a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(a__sqr(mark(z - 2)))) :|: z - 2 >= 0 a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(a__half(mark(z - 2)))) :|: z - 2 >= 0 a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(a__first(mark(X110), mark(X26)))) :|: X110 >= 0, X26 >= 0, z = 1 + (1 + X110 + X26) a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(a__dbl(mark(z - 2)))) :|: z - 2 >= 0 a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(a__add(mark(X19), mark(X25)))) :|: z = 1 + (1 + X19 + X25), X19 >= 0, X25 >= 0 a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(1)) :|: z = 1 + 1 a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(0)) :|: z = 1 + 0 a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(1 + mark(z - 2))) :|: z - 2 >= 0 a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(1 + mark(X111) + X28)) :|: X28 >= 0, z = 1 + (1 + X111 + X28), X111 >= 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__half(z) -{ 1 }-> mark(z - 1) :|: z - 1 >= 0 a__half(z) -{ 1 }-> 0 :|: z = 0 a__half(z) -{ 1 }-> 0 :|: z = 1 + 0 a__half(z) -{ 1 }-> 1 + z :|: z >= 0 a__half(z) -{ 2 }-> 1 + a__half(a__terms(mark(z - 3))) :|: z - 3 >= 0 a__half(z) -{ 2 }-> 1 + a__half(a__sqr(mark(z - 3))) :|: z - 3 >= 0 a__half(z) -{ 2 }-> 1 + a__half(a__half(mark(z - 3))) :|: z - 3 >= 0 a__half(z) -{ 2 }-> 1 + a__half(a__first(mark(X149), mark(X247))) :|: X149 >= 0, X247 >= 0, z = 1 + (1 + (1 + X149 + X247)) a__half(z) -{ 2 }-> 1 + a__half(a__dbl(mark(z - 3))) :|: z - 3 >= 0 a__half(z) -{ 2 }-> 1 + a__half(a__add(mark(X148), mark(X246))) :|: X246 >= 0, X148 >= 0, z = 1 + (1 + (1 + X148 + X246)) a__half(z) -{ 2 }-> 1 + a__half(1) :|: z = 1 + (1 + 1) a__half(z) -{ 2 }-> 1 + a__half(0) :|: z = 1 + (1 + 0) a__half(z) -{ 2 }-> 1 + a__half(1 + mark(z - 3)) :|: z - 3 >= 0 a__half(z) -{ 2 }-> 1 + a__half(1 + mark(X150) + X248) :|: X248 >= 0, X150 >= 0, z = 1 + (1 + (1 + X150 + X248)) a__sqr(z) -{ 1 }-> 0 :|: z = 0 a__sqr(z) -{ 1 }-> 1 + z :|: z >= 0 a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(a__terms(mark(z - 2))), a__dbl(a__terms(mark(z - 2)))) :|: z - 2 >= 0 a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(a__sqr(mark(z - 2))), a__dbl(a__sqr(mark(z - 2)))) :|: z - 2 >= 0 a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(a__half(mark(z - 2))), a__dbl(a__half(mark(z - 2)))) :|: z - 2 >= 0 a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(a__first(mark(X13), mark(X23))), a__dbl(a__first(mark(X13), mark(X23)))) :|: z = 1 + (1 + X13 + X23), X13 >= 0, X23 >= 0 a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(a__dbl(mark(z - 2))), a__dbl(a__dbl(mark(z - 2)))) :|: z - 2 >= 0 a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(a__add(mark(X12), mark(X22))), a__dbl(a__add(mark(X12), mark(X22)))) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(1), a__dbl(1)) :|: z = 1 + 1 a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(0), a__dbl(0)) :|: z = 1 + 0 a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(1 + mark(z - 2)), a__dbl(1 + mark(z - 2))) :|: z - 2 >= 0 a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(1 + mark(X14) + X24), a__dbl(1 + mark(X14) + X24)) :|: z = 1 + (1 + X14 + X24), X14 >= 0, X24 >= 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__half(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)) + (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 + 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 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__half(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__terms(a__first(mark(X154), mark(X250))) :|: X154 >= 0, z = 1 + (1 + X154 + X250), X250 >= 0 mark(z) -{ 2 }-> a__terms(a__dbl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__terms(a__add(mark(X152), mark(X249))) :|: z = 1 + (1 + X152 + X249), X152 >= 0, X249 >= 0 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 + mark(X156) + X251) :|: X156 >= 0, X251 >= 0, z = 1 + (1 + X156 + X251) 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__half(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__sqr(a__first(mark(X163), mark(X253))) :|: X163 >= 0, X253 >= 0, z = 1 + (1 + X163 + X253) mark(z) -{ 2 }-> a__sqr(a__dbl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__sqr(a__add(mark(X161), mark(X252))) :|: X252 >= 0, z = 1 + (1 + X161 + X252), X161 >= 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 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__sqr(1 + mark(X165) + X254) :|: X165 >= 0, z = 1 + (1 + X165 + X254), X254 >= 0 mark(z) -{ 2 }-> a__half(a__terms(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__half(a__sqr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__half(a__half(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__half(a__first(mark(X1165), mark(X2151))) :|: z = 1 + (1 + X1165 + X2151), X2151 >= 0, X1165 >= 0 mark(z) -{ 2 }-> a__half(a__dbl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__half(a__add(mark(X1164), mark(X2150))) :|: X1164 >= 0, X2150 >= 0, z = 1 + (1 + X1164 + X2150) mark(z) -{ 2 }-> a__half(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__half(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__half(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__half(1 + mark(X1166) + X2152) :|: X2152 >= 0, X1166 >= 0, z = 1 + (1 + X1166 + X2152) 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__half(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__dbl(a__first(mark(X1126), mark(X2112))) :|: z = 1 + (1 + X1126 + X2112), X2112 >= 0, X1126 >= 0 mark(z) -{ 2 }-> a__dbl(a__dbl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__dbl(a__add(mark(X1125), mark(X2111))) :|: X1125 >= 0, X2111 >= 0, z = 1 + (1 + X1125 + X2111) mark(z) -{ 2 }-> a__dbl(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__dbl(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__dbl(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__dbl(1 + mark(X1127) + X2113) :|: X2113 >= 0, X1127 >= 0, z = 1 + (1 + X1127 + X2113) 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 + mark(z - 1) :|: z - 1 >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 ---------------------------------------- (257) 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 ---------------------------------------- (258) 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(a__add(a__sqr(mark(X)), a__dbl(mark(X)))) [1] a__dbl(0) -> 0 [1] a__dbl(s(X)) -> s(s(a__dbl(mark(X)))) [1] a__add(0, X) -> mark(X) [1] a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) [1] a__first(0, X) -> nil [1] a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1] a__half(0) -> 0 [1] a__half(s(0)) -> 0 [1] a__half(s(s(X))) -> s(a__half(mark(X))) [1] a__half(dbl(X)) -> mark(X) [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(half(X)) -> a__half(mark(X)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(recip(X)) -> recip(mark(X)) [1] mark(s(X)) -> s(mark(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] a__half(X) -> half(X) [1] The TRS has the following type information: a__terms :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half cons :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half recip :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half a__sqr :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half mark :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half terms :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half s :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half 0 :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half a__add :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half a__dbl :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half a__first :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half nil :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half first :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half a__half :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half dbl :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half sqr :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half add :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half half :: recip:s:terms:cons:0:nil:first:dbl:sqr:add:half -> recip:s:terms:cons:0:nil:first:dbl:sqr:add:half Rewrite Strategy: INNERMOST ---------------------------------------- (259) 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 ---------------------------------------- (260) Obligation: Complexity RNTS consisting of the following rules: a__add(z, z') -{ 1 }-> mark(X) :|: z' = X, X >= 0, z = 0 a__add(z, z') -{ 1 }-> 1 + a__add(mark(X), mark(Y)) :|: z = 1 + X, z' = Y, Y >= 0, X >= 0 a__add(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__dbl(z) -{ 1 }-> 0 :|: z = 0 a__dbl(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__dbl(z) -{ 1 }-> 1 + (1 + a__dbl(mark(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__half(z) -{ 1 }-> mark(X) :|: z = 1 + X, X >= 0 a__half(z) -{ 1 }-> 0 :|: z = 0 a__half(z) -{ 1 }-> 0 :|: z = 1 + 0 a__half(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__half(z) -{ 1 }-> 1 + a__half(mark(X)) :|: z = 1 + (1 + X), X >= 0 a__sqr(z) -{ 1 }-> 0 :|: z = 0 a__sqr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__sqr(z) -{ 1 }-> 1 + a__add(a__sqr(mark(X)), a__dbl(mark(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__half(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 + 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.