KILLED proof of input_f6qZcIAVQr.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 169 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 13 ms] (14) CpxRNTS (15) SimplificationProof [BOTH BOUNDS(ID, ID), 19 ms] (16) CpxRNTS (17) CompletionProof [UPPER BOUND(ID), 0 ms] (18) CpxTypedWeightedCompleteTrs (19) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (20) CpxRNTS (21) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (22) CdtProblem (23) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CdtProblem (25) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CdtProblem (27) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CdtProblem (29) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CdtProblem (31) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CdtProblem (33) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CdtProblem (35) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CdtProblem (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 3 ms] (38) CdtProblem (39) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms] (50) CdtProblem (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (52) CdtProblem (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 41 ms] (72) CdtProblem (73) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 56 ms] (78) CdtProblem (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8 ms] (82) CdtProblem (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms] (88) CdtProblem (89) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 42 ms] (94) CdtProblem (95) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 21 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 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) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18 ms] (110) CdtProblem (111) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 ms] (122) CdtProblem (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 143 ms] (130) CdtProblem (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 64 ms] (134) CdtProblem (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 73 ms] (138) CdtProblem (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 19 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 133 ms] (142) CdtProblem (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 62 ms] (146) CdtProblem (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 219 ms] (150) CdtProblem (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 35 ms] (152) CdtProblem (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 99 ms] (154) CdtProblem (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (156) CdtProblem (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 99 ms] (158) CdtProblem (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 33 ms] (160) CdtProblem (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 98 ms] (162) CdtProblem (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 41 ms] (164) CdtProblem (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 203 ms] (166) CdtProblem (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 58 ms] (168) CdtProblem (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 173 ms] (170) CdtProblem (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 24 ms] (172) CdtProblem (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 122 ms] (174) CdtProblem (175) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 50 ms] (176) CdtProblem (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 327 ms] (178) CdtProblem (179) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 25 ms] (180) CdtProblem (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 253 ms] (182) CdtProblem (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 64 ms] (184) CdtProblem (185) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 331 ms] (186) CdtProblem (187) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 34 ms] (188) CdtProblem (189) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 218 ms] (190) CdtProblem (191) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (192) CdtProblem (193) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 295 ms] (194) CdtProblem (195) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 64 ms] (196) CdtProblem (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 238 ms] (198) CdtProblem (199) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 77 ms] (200) CdtProblem (201) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 280 ms] (202) CdtProblem (203) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 53 ms] (204) CdtProblem ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__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) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__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 ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__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 ---------------------------------------- (9) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: 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 ---------------------------------------- (10) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__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 ---------------------------------------- (11) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (12) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__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 ---------------------------------------- (13) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 nil => 1 ---------------------------------------- (14) Obligation: Complexity RNTS consisting of the following rules: a__add(z, z') -{ 1 }-> mark(X) :|: z' = X, X >= 0, z = 0 a__add(z, z') -{ 1 }-> 1 + a__add(mark(X), mark(Y)) :|: z = 1 + X, z' = Y, Y >= 0, X >= 0 a__add(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__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 ---------------------------------------- (15) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (16) 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 ---------------------------------------- (17) 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 ---------------------------------------- (18) 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 ---------------------------------------- (19) 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 ---------------------------------------- (20) 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. ---------------------------------------- (21) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (22) 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 ---------------------------------------- (23) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 13 trailing nodes: A__DBL(z0) -> c8 A__FIRST(z0, z1) -> c15 A__DBL(0) -> c6 MARK(0) -> c32 A__HALF(0) -> c16 A__HALF(s(0)) -> c17 A__SQR(z0) -> c5 A__ADD(z0, z1) -> c12 A__HALF(z0) -> c20 A__SQR(0) -> c2 MARK(nil) -> c33 A__TERMS(z0) -> c1 A__FIRST(0, z0) -> c13 ---------------------------------------- (24) 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 ---------------------------------------- (25) 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)) ---------------------------------------- (26) 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 ---------------------------------------- (27) 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)) ---------------------------------------- (28) 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 ---------------------------------------- (29) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (30) 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 ---------------------------------------- (31) 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)) ---------------------------------------- (32) 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 ---------------------------------------- (33) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (34) 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 ---------------------------------------- (35) 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)) ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(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 ---------------------------------------- (37) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(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 ---------------------------------------- (39) 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)) ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(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 ---------------------------------------- (41) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__DBL(s(0)) -> c7(A__DBL(0), MARK(0)) A__DBL(s(nil)) -> c7(A__DBL(nil), MARK(nil)) ---------------------------------------- (42) 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 ---------------------------------------- (43) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (44) 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 ---------------------------------------- (45) 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)) ---------------------------------------- (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__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 ---------------------------------------- (47) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__ADD(s(nil), x1) -> c10(A__ADD(nil, mark(x1)), MARK(nil)) ---------------------------------------- (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__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 ---------------------------------------- (49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (50) 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 ---------------------------------------- (51) 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)) ---------------------------------------- (52) 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 ---------------------------------------- (53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (54) 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 ---------------------------------------- (55) 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)) ---------------------------------------- (56) 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 ---------------------------------------- (57) 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)) ---------------------------------------- (58) 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 ---------------------------------------- (59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (60) 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 ---------------------------------------- (61) 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)) ---------------------------------------- (62) 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 ---------------------------------------- (63) 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)) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(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 ---------------------------------------- (65) 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)) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(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 ---------------------------------------- (67) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(sqr(0)) -> c22(A__SQR(0), MARK(0)) MARK(sqr(nil)) -> c22(A__SQR(nil), MARK(nil)) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(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 ---------------------------------------- (69) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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__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 ---------------------------------------- (71) 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)) ---------------------------------------- (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__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 ---------------------------------------- (73) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(add(nil, x1)) -> c23(A__ADD(nil, mark(x1)), MARK(nil)) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(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 ---------------------------------------- (75) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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__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 ---------------------------------------- (77) 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)) ---------------------------------------- (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__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 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (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__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 ---------------------------------------- (81) 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)) ---------------------------------------- (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__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 ---------------------------------------- (83) 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)) ---------------------------------------- (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__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 ---------------------------------------- (85) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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__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 ---------------------------------------- (87) 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)) ---------------------------------------- (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__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 ---------------------------------------- (89) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(nil, x1)) -> c26(A__FIRST(nil, mark(x1)), MARK(nil)) MARK(first(0, x1)) -> c26(A__FIRST(0, mark(x1)), MARK(0)) ---------------------------------------- (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__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 ---------------------------------------- (91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (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__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 ---------------------------------------- (93) 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)) ---------------------------------------- (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__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 ---------------------------------------- (95) 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)) ---------------------------------------- (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(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 ---------------------------------------- (97) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 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(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 ---------------------------------------- (99) 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)) ---------------------------------------- (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(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 ---------------------------------------- (101) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(half(nil)) -> c28(A__HALF(nil), MARK(nil)) MARK(half(0)) -> c28(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(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 ---------------------------------------- (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(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 ---------------------------------------- (105) 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))) ---------------------------------------- (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(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 ---------------------------------------- (107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(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 ---------------------------------------- (109) 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))) ---------------------------------------- (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(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 ---------------------------------------- (111) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (113) 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))) ---------------------------------------- (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(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 ---------------------------------------- (115) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (117) 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))) ---------------------------------------- (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(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))) 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 ---------------------------------------- (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(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))) -> 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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 ---------------------------------------- (121) 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))) ---------------------------------------- (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(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 ---------------------------------------- (123) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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(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)) -> 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))) 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 ---------------------------------------- (125) 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))) ---------------------------------------- (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(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 ---------------------------------------- (127) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (129) 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)) ---------------------------------------- (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(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(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 ---------------------------------------- (131) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(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 ---------------------------------------- (133) 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))) ---------------------------------------- (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(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 ---------------------------------------- (135) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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(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 ---------------------------------------- (137) 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))) ---------------------------------------- (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(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 ---------------------------------------- (139) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (141) 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))) ---------------------------------------- (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(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 ---------------------------------------- (143) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(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 ---------------------------------------- (145) 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))) ---------------------------------------- (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(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 ---------------------------------------- (147) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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(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 ---------------------------------------- (149) 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))) ---------------------------------------- (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(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 ---------------------------------------- (151) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(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 ---------------------------------------- (153) 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))) ---------------------------------------- (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(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 ---------------------------------------- (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(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 ---------------------------------------- (157) 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))) ---------------------------------------- (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(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 ---------------------------------------- (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(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 ---------------------------------------- (161) 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))) ---------------------------------------- (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(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 ---------------------------------------- (163) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(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 ---------------------------------------- (165) 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))) ---------------------------------------- (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(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 ---------------------------------------- (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(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 ---------------------------------------- (169) 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))) ---------------------------------------- (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(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 ---------------------------------------- (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(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 ---------------------------------------- (173) 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))) ---------------------------------------- (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(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 ---------------------------------------- (175) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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(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 ---------------------------------------- (177) 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))) ---------------------------------------- (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(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 ---------------------------------------- (179) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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(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 ---------------------------------------- (181) 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))) ---------------------------------------- (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(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 ---------------------------------------- (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(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 ---------------------------------------- (185) 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))) ---------------------------------------- (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(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 ---------------------------------------- (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(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 ---------------------------------------- (189) 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))) ---------------------------------------- (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(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 ---------------------------------------- (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(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 ---------------------------------------- (193) 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))) ---------------------------------------- (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(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 ---------------------------------------- (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(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 ---------------------------------------- (197) 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))) ---------------------------------------- (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(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 ---------------------------------------- (199) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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(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 ---------------------------------------- (201) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace 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))) by A__SQR(s(s(x0))) -> c3(A__ADD(a__sqr(s(mark(x0))), dbl(mark(s(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))) A__SQR(s(s(x0))) -> c3(A__ADD(s(a__add(a__sqr(mark(mark(x0))), a__dbl(mark(mark(x0))))), a__dbl(mark(s(x0)))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(sqr(s(mark(x0))), a__dbl(mark(s(x0)))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(s(a__terms(mark(z0)))), a__dbl(mark(s(terms(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(s(a__sqr(mark(z0)))), a__dbl(mark(s(sqr(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(s(a__add(mark(z0), mark(z1)))), a__dbl(mark(s(add(z0, z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(s(a__dbl(mark(z0)))), a__dbl(mark(s(dbl(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(s(a__first(mark(z0), mark(z1)))), a__dbl(mark(s(first(z0, z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(s(a__half(mark(z0)))), a__dbl(mark(s(half(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(s(cons(mark(z0), z1))), a__dbl(mark(s(cons(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(s(recip(mark(z0)))), a__dbl(mark(s(recip(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(s(s(mark(z0)))), a__dbl(mark(s(s(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(s(0)), a__dbl(mark(s(0)))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(s(nil)), a__dbl(mark(s(nil)))), A__SQR(mark(s(nil))), MARK(s(nil))) ---------------------------------------- (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(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))) A__SQR(s(s(x0))) -> c3(A__ADD(s(a__add(a__sqr(mark(mark(x0))), a__dbl(mark(mark(x0))))), a__dbl(mark(s(x0)))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(sqr(s(mark(x0))), a__dbl(mark(s(x0)))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(s(a__terms(mark(z0)))), a__dbl(mark(s(terms(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(s(a__sqr(mark(z0)))), a__dbl(mark(s(sqr(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(s(a__add(mark(z0), mark(z1)))), a__dbl(mark(s(add(z0, z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(s(a__dbl(mark(z0)))), a__dbl(mark(s(dbl(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(s(a__first(mark(z0), mark(z1)))), a__dbl(mark(s(first(z0, z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(s(a__half(mark(z0)))), a__dbl(mark(s(half(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(s(cons(mark(z0), z1))), a__dbl(mark(s(cons(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(s(recip(mark(z0)))), a__dbl(mark(s(recip(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(s(s(mark(z0)))), a__dbl(mark(s(s(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(s(0)), a__dbl(mark(s(0)))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(s(nil)), a__dbl(mark(s(nil)))), A__SQR(mark(s(nil))), MARK(s(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(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))) A__SQR(s(s(x0))) -> c3(A__ADD(s(a__add(a__sqr(mark(mark(x0))), a__dbl(mark(mark(x0))))), a__dbl(mark(s(x0)))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(x0))) -> c3(A__ADD(sqr(s(mark(x0))), a__dbl(mark(s(x0)))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(s(a__terms(mark(z0)))), a__dbl(mark(s(terms(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(s(a__sqr(mark(z0)))), a__dbl(mark(s(sqr(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(s(a__add(mark(z0), mark(z1)))), a__dbl(mark(s(add(z0, z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(s(a__dbl(mark(z0)))), a__dbl(mark(s(dbl(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(s(a__first(mark(z0), mark(z1)))), a__dbl(mark(s(first(z0, z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(s(a__half(mark(z0)))), a__dbl(mark(s(half(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(s(cons(mark(z0), z1))), a__dbl(mark(s(cons(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(s(recip(mark(z0)))), a__dbl(mark(s(recip(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(s(s(mark(z0)))), a__dbl(mark(s(s(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(s(0)), a__dbl(mark(s(0)))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(s(nil)), a__dbl(mark(s(nil)))), A__SQR(mark(s(nil))), MARK(s(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_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, c3_3 ---------------------------------------- (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(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))) A__SQR(s(s(x0))) -> c3(A__ADD(s(a__add(a__sqr(mark(mark(x0))), a__dbl(mark(mark(x0))))), a__dbl(mark(s(x0)))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(s(a__terms(mark(z0)))), a__dbl(mark(s(terms(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(s(a__sqr(mark(z0)))), a__dbl(mark(s(sqr(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(s(a__add(mark(z0), mark(z1)))), a__dbl(mark(s(add(z0, z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(s(a__dbl(mark(z0)))), a__dbl(mark(s(dbl(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(s(a__first(mark(z0), mark(z1)))), a__dbl(mark(s(first(z0, z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(s(a__half(mark(z0)))), a__dbl(mark(s(half(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(s(cons(mark(z0), z1))), a__dbl(mark(s(cons(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(s(recip(mark(z0)))), a__dbl(mark(s(recip(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(s(s(mark(z0)))), a__dbl(mark(s(s(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(s(0)), a__dbl(mark(s(0)))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(s(nil)), a__dbl(mark(s(nil)))), A__SQR(mark(s(nil))), MARK(s(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(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(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))) A__SQR(s(s(x0))) -> c3(A__ADD(s(a__add(a__sqr(mark(mark(x0))), a__dbl(mark(mark(x0))))), a__dbl(mark(s(x0)))), A__SQR(mark(s(x0))), MARK(s(x0))) A__SQR(s(s(terms(z0)))) -> c3(A__ADD(a__sqr(s(a__terms(mark(z0)))), a__dbl(mark(s(terms(z0))))), A__SQR(mark(s(terms(z0)))), MARK(s(terms(z0)))) A__SQR(s(s(sqr(z0)))) -> c3(A__ADD(a__sqr(s(a__sqr(mark(z0)))), a__dbl(mark(s(sqr(z0))))), A__SQR(mark(s(sqr(z0)))), MARK(s(sqr(z0)))) A__SQR(s(s(add(z0, z1)))) -> c3(A__ADD(a__sqr(s(a__add(mark(z0), mark(z1)))), a__dbl(mark(s(add(z0, z1))))), A__SQR(mark(s(add(z0, z1)))), MARK(s(add(z0, z1)))) A__SQR(s(s(dbl(z0)))) -> c3(A__ADD(a__sqr(s(a__dbl(mark(z0)))), a__dbl(mark(s(dbl(z0))))), A__SQR(mark(s(dbl(z0)))), MARK(s(dbl(z0)))) A__SQR(s(s(first(z0, z1)))) -> c3(A__ADD(a__sqr(s(a__first(mark(z0), mark(z1)))), a__dbl(mark(s(first(z0, z1))))), A__SQR(mark(s(first(z0, z1)))), MARK(s(first(z0, z1)))) A__SQR(s(s(half(z0)))) -> c3(A__ADD(a__sqr(s(a__half(mark(z0)))), a__dbl(mark(s(half(z0))))), A__SQR(mark(s(half(z0)))), MARK(s(half(z0)))) A__SQR(s(s(cons(z0, z1)))) -> c3(A__ADD(a__sqr(s(cons(mark(z0), z1))), a__dbl(mark(s(cons(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(s(recip(mark(z0)))), a__dbl(mark(s(recip(z0))))), A__SQR(mark(s(recip(z0)))), MARK(s(recip(z0)))) A__SQR(s(s(s(z0)))) -> c3(A__ADD(a__sqr(s(s(mark(z0)))), a__dbl(mark(s(s(z0))))), A__SQR(mark(s(s(z0)))), MARK(s(s(z0)))) A__SQR(s(s(0))) -> c3(A__ADD(a__sqr(s(0)), a__dbl(mark(s(0)))), A__SQR(mark(s(0))), MARK(s(0))) A__SQR(s(s(nil))) -> c3(A__ADD(a__sqr(s(nil)), a__dbl(mark(s(nil)))), A__SQR(mark(s(nil))), MARK(s(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_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, c3_3